rationalise and find a and b. √11-√7/√11+√7=a-b √77
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a = 9 / 2 , b = 1 / 2
Step-by-step explanation:
√11 - √7 / √11 + √7 = a - √77 b
LHS = √11 - √7 / √11 + √7
= √11 - √7 / √11 + √7 × √11 - √7 / √11 - √7
= (√11 - √7)² / (√11)² - (√7)²
= (√11)² + (√7)² - 2×(√11)×(√7) / 11 - 7
= 11 + 7 - 2√77 / 4
= 18 - 2√77 / 4
= 18 / 4 - 2√77 / 4
= 9 / 2 - √77 / 2 --- (Compare with RHS)
9 / 2 - √77 / 2 = a - √77 b
a = 9 / 2 , b = 1 / 2
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