Question

what will be the value of a and b if :√5+3/√5+7 =a-b √5
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Answer 1

Answer:

Step-by-step explanation:

Given

3+5–√3−5–√=a+b5–√

Take the conjugate of the denominator term and multiply both numerator and denominator by that conjugate.

Here, conjugate of 3−5–√ is 3+5–√ .

Now,

(3+5–√3−5–√)×(3+5–√3+5–√)=a+b5–√

⟹(3+5–√)2(3−5–√)(3+5–√)=a+b5–√

We know

(a+b)2=a2+b2+2ab⋯(1)

(a+b)(a−b)=a2−b2⋯(2)

Apply formula (1) in the numerator and formula (2) in the denominator.

(3)2+(5–√)2+2×3×5–√32−(5–√)2=a+b5–√

9+5+65–√9−5=a+b5–√

⟹14+65–√4=a+b5–√

Take 2 as common from the numerator.

2(7+35–√)4=a+b5–√

⟹7+35–√2=a+b5–√

⟹72+325–√=a+b5–√

Comparing the corresponding rational and irrational parts on both sides, we get:

a=72,b=32

or

a=3.5,b=1.5