Question

Plz solve this... fast

Answer 1

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1. given :- (√7 - 2)/(√7 + 2) = a√7 + b

LHS :-

= (√7 - 2)/(√7 + 2) × (√7 - 2)/(√7 - 2)

= (√7 - 2)(√7 - 2)/(√7 + 2)(√7 - 2)

= (√7 - 2)²/(√7)²-(2)²

= (7 - 4√7 + 4)/(7 - 4)

= (11 - 4√7)/3

= 11/3 - 4√7/3

we can also write it as,

= -4√7/3 + 11/3

comparing with RHS

⏩ -4√7/3 + 11/3 = a√7 + b

⏩ a = -4/3 and b = 11/3

2. given :-

(5 + 3√2)/(5 - 3√2) = a + b√2

LHS :-

= (5 + 3√2)/(5 - 3√2) × (5 + 3√2)/(5 + 3√2)

= (5 + 3√2)(5 + 3√2)/(5 - 3√2)(5 + 3√2)

= (5 + 3√2)²/(5)²-(3√2)²

= (25 + 2(5)(3√2) + 18)/(25 - 18)

= (43 + 30√2)/7

= 43/7 + 30√2/7

comparing LHS with RHS :-

⏩ 43/7 + 30√2/7 = a + b√7

⏩ a = 43/7 and b = 30/7