Question

if √7 - √6/√7+√6=a+b√42 then a= and b= ?

Answer 1

Heya !!!



✓7 - ✓6 / ✓7 + ✓6 = A + B✓42



LHS = ✓7 - ✓6 / ✓7 + ✓6



Rationalizing the denominator ✓7 + ✓6





=> ✓7 - ✓6 / ✓7 + ✓6 × ( ✓7 - ✓6 ) / ( ✓7 - ✓6 )




=> ( ✓7 - ✓6 ) ( ✓7 - ✓6 ) / ( ✓7 + ✓6 ) (✓7-✓6 )




=> ( ✓7 - ✓6)² / ( ✓7)² - (✓6)²




=> (✓7)² + (✓6)² - 2 × ✓7 × ✓6 / 7-6




=> 7 + 6 - 2✓42/1




=> 13 - 2✓42


Now,



LHS = RHS


13 - 2✓42 = A - B✓42



Clearly,



A = 13 and B = 2



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