Question

solve 2^(2x+3)-65^(2x-1)=57​

Answer 1

hey mate..

your answer:-

22x+3 − 65(2x−1) = 57

⇒22x . 23 − 65(2x−1) = 57

⇒(2x)2 . 8 − 65(2x−1) = 57

Put 2x = y in the above equation, we get:-

⇒y2 . 8 − 65(y − 1) = 57

⇒8y2 − 65y + 65 = 57

⇒8y2 − 65y + 8 = 0

⇒8y2 − 64y − y + 8 = 0

⇒8y(y − 8) − 1(y − 8) = 0

⇒(8y − 1)(y − 8) = 0

⇒8y − 1 = 0 or y − 8 = 0

⇒y = 18 or y = 8

⇒2x = 123 or 2x = 23

⇒2x = 2−3 or 2x = 23

⇒x = −3 or x = 3