If ₃ 2, ₃ (2^x-5 ) and ₃ (2^x- 7 2 ) are in AP , the value of x is

Step-by-step solution

aligned & ₃ 2, ₃ (2^x-5 ), ₃ (2^x- 7 2 ) are in AP. & ₃ (2^x-5 )= ₃ (2^x- 7 2 )+ ₃ 2 2 & (2^x-5 )^2=2 (2^x- 7 2 ) & (2^x )^2+25-10 2^x=2 2^x-7 & (2^x )^2-12 2^x+25+7=0 & (2^x )^2-12 2^x+32=0 & 2^x=8 or 2^x=4 & x=3 or 2 & x=3( x=2 does not satisfy the given series ) aligned