Question

2+5underroot7upon 2-5underroot7is equal to a+underroot7b find a and b​

Answer 1

Solution:

LHS = (2+5√7)/(2-5√7)

Rationalising the denominator, we get

= [(2+5√7)(2+5√7)]/[(2-5√7)(2+5√7)]

= (2+5√7)²/[2²-(5√7)²]

= [2²+(5√7)²+2*2*5√7]/(4-175)

= (4+175+20√7)/(-171)

= (179+20√7)/(-171)

= (179/(-171)+(20/-171)√7

Now ,

(179/(-171)+(20/-171)√7=a+7√b

compare both sides, we get

a = -179/171, b = -20/171

Therefore,

a = -179/171 , b = -20/171

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