Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

If sum of the roots of the equation 2 (4^x-2 )= 8+ (4^x- 31 8 ) lies between two consecutive natural numbers a and b , then find the value of (a+b) .

Correct answer

Step-by-step solution

aligned & (4^x-2 )^2= (8 (4^x- 31 8 ) ) & (4^x-2 )^2=8 4^x-31 & 4^x=t & (t-2)^2=8 t-31 & t^2-12 t+35=0 t=5,7 & 4^x=5,7 x= ₄ 5, ₄ 7 & Sum of the roots = ₄ 5+ ₄ 7= ₄ 35 (2,3) (a, b) & a+b=5 & aligned Let

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