Question

if a =√7-√6/ √7+√6 and b=√7+√6/√7-√6 then find a^2+b^2+ab

Answer 1

Hey!! Here's the solution :D

a = (√7 - √6) / (√7 + √6)

(Rationalize the denominator )

a = (√7 - √6)² / (√7 + √6)( √7 - √6)

= 7 + 6 - 2√42

= 13 - 2√42

b = (√7 + √6) / (√7 - √6)

= (√7 + √6)² / (√7 - √6)( √7 + √6)

= 13 + 2√42

Now substitute the values in the given equation ; i.e., a² + b² + ab

= (13 - 2√42)² + (13 + 2√42)² + (13 - 2√42)(13 + 2√42)

= (169 + 168 - 52√42) + (169 + 168 + 52√42) + (169 + 168)

= 1011

Ans. = 1011

Hope it helps! ^^

Answer 2

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a = (√7 - √6) / (√7 + √6)

(Rationalize the denominator )

a = (√7 - √6)² / (√7 + √6)( √7 - √6)

= 7 + 6 - 2√42

= 13 - 2√42

b = (√7 + √6) / (√7 - √6)

= (√7 + √6)² / (√7 - √6)( √7 + √6)

= 13 + 2√42

Now substitute the values in the given equation ; i.e., a² + b² + ab

= (13 - 2√42)² + (13 + 2√42)² + (13 - 2√42)(13 + 2√42)

= (169 + 168 - 52√42) + (169 + 168 + 52√42) + (169 + 168)

= 1011