Question

if A and B are rational numbers find the value of A and B in each of the following equalities 3+√7/3-√7=a+b√7​

Answer 1

Answer:

a=3 and b=5 is the correct answer to the question

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Answer 2

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