Question

if 1 by 2 + root 22 + root 26 equal to 1 by root a into b square into root a + root b minus whole root a + b then what are the values of a and b.

Answer 1

Answer:

a = 22 and b = 4

Step-by-step explanation:

Now, 1/(2 + √22 + √26)

= 1/{(√22 + 2) + √26}

= {(√22 + 2) - √26}/[{(√22 + 2) + √26)}{(√22 + 2) - √26}],

by multiplying {(√22 + 2) - √26} to both the numerator and the denominator by the conjugate of the denominator

= {(√22 + 2) - √26}/(22 + 4 + 4√22 - 26)

= {√22 + √4 - √(22 + 4)}/(4√22)

= {√22 + √4 - √(22 + 4)}/(√22 × 2²)

By the given condition,

{√22 + √4 - √(22 + 4)}/(√22 × 2²)

= {√a + √b - √(a + b)}/(√a × b²)

Comparing from both sides, we get

a = 22 and b = 4