[Akriti]

1. the 100th root of 10⁽¹⁰¹⁰) is:

2. Sum of all integers less than 100 which when divided by3 leave a remainder 1 and 2 when divided by 4:

3. Square root of 2 raised to power x + Square root of 3 raised to power x = Square root of 10 raised to power x/2. Find the value of x.

4.if x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have common root , then the value of a is:

5.If one root of a quadratic equation is 1/sq root of 4 - sq root of3, then the equation is:

The three sides of a right triangle have integral lengths that are in A.P.(arithematic progression). Then one of the sides is

a. 22 b.58 c.81 d.91

ALL THE BEST!

I AM READY TO RECEIVE YOUR ANSWERS!@#!@

Edited November 15, 2010 by Akriti

[Guest]

1. The 100th root of X is simply X^1/100. So the 100th root of 10¹⁰¹⁰ would be 10¹⁰⁸

2. Let N be a number with the mentioned properties. N + 2 = 3K₁, where K₁ is a natual number, and N + 2 = 4K₂, where K₂ is also a natural number. So N + 2 can be divided by 3x4 = 12. the multiples of 12 that are smaller than 100 are 12,24,36,48,60,72,84 and 96. Using the sum of an AP, we find that the sum of these numbers is (12+96)(8/2) = 432. Subtracting 2 for each number, we get the sum we're looking for, which is 416.

Edited November 15, 2010 by archlordbr

[Guest]

This sounds like homework. There's a separate forum for homework help, but don't ask people to do your work for you.

[Guest]

Agree with the above answers for first two parts

3)

No solution for integer x

2^x will be even

3^x will be odd

you can figure out the rest of the reasoning

4) a = +1 or -1

since it sounds like homework, I'll let you figure out why

5)

x² - 4x + 1

Again, I'll let you figure out why

6) 81 is one of the sides.

And again, .... you know what

Edited November 15, 2010 by DeeGee

[Guest]

Agree with the above answers for first two parts

3)

No solution for integer x

2^x will be even

3^x will be odd

you can figure out the rest of the reasoning

4) a = +1 or -1

since it sounds like homework, I'll let you figure out why

5)

x² - 4x + 1

Again, I'll let you figure out why

if a quadratic equation has 1 root in the form of a+ib, then there is always another root in the form a-ib. If you know the roots finding equation is straight forward

6) 81 is one of the sides.

And again, .... you know what

[Guest]

1. the 100th root of 10⁽¹⁰¹⁰) is:

2. Sum of all integers less than 100 which when divided by3 leave a remainder 1 and 2 when divided by 4:

3. Square root of 2 raised to power x + Square root of 3 raised to power x = Square root of 10 raised to power x/2. Find the value of x.

4.if x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have common root , then the value of a is:

5.If one root of a quadratic equation is 1/sq root of 4 - sq root of3, then the equation is:

The three sides of a right triangle have integral lengths that are in A.P.(arithematic progression). Then one of the sides is

a. 22 b.58 c.81 d.91

ALL THE BEST!

I AM READY TO RECEIVE YOUR ANSWERS!@#!@

1. 100th root of 10⁽¹⁰¹⁰) == 100th root of 10¹⁰⁰ == 10^100/100 == 10¹ == 10

2. Set S of all Integers x < 100 such that x mod 3 == 1 {1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 76, 79, 82, 85, 88, 91, 94, 97}

Of these the ones y such that y mod 4 == 2 (every 4th one) {10, 22, 34, 46, 58, 70, 82, 94}

Therefore SUM(10+22+34+46+58+70+82+94) = 416

[Guest]

1. the 100th root of 10⁽¹⁰¹⁰) is:

2. Sum of all integers less than 100 which when divided by3 leave a remainder 1 and 2 when divided by 4:

3. Square root of 2 raised to power x + Square root of 3 raised to power x = Square root of 10 raised to power x/2. Find the value of x.

4.if x² + 4ax + 3 = 0 and 2x² + 3ax - 9 = 0 have common root , then the value of a is:

5.If one root of a quadratic equation is 1/sq root of 4 - sq root of3, then the equation is:

The three sides of a right triangle have integral lengths that are in A.P.(arithematic progression). Then one of the sides is

a. 22 b.58 c.81 d.91

ALL THE BEST!

I AM READY TO RECEIVE YOUR ANSWERS!@#!@

4. I believe the answer is a = 0. That assumes that the quadratics have one real root x and that it is the same for both equations

Edited November 15, 2010 by Justgus

[Akriti]

Sorry, J.green. But I found these questions in the sample paper of International Mathematics Olympiad and I was not ableto get it. So I thought to sought some help from geniuses.

[Guest]

Sorry, J.green. But I found these questions in the sample paper of International Mathematics Olympiad and I was not ableto get it. So I thought to sought some help from geniuses.

Oh, I tried the Brazilian olympiad once. Got 12 out of 25 on phase 1, which was exactly the minimum score to get to phase 2, that year. Then on phase 2 I got a nice 0. I could only do 1 question, but I made a little mistake in the end and gave a wrong answer. That's when I realized math was not for me...