Answer:
3 and -3
Explanation:
hello : 2^(2x+3) - 57=65(2^x-1)
look : 2^2x = (2^x)² and 2^(2x+3) = 2^2x × 2^3 =8(2^x)²
now let ; 2^x =t ....(t > 0)
8t²- 57 = 65(t - 1)
8t² -65t +8 = 0
quadratic equation : Δ = b²-4ac when : a =8 and b = -65 and c= 8
Δ = (-65)²-4(8)(8) = 4225-256=3969 =63²
√Δ =63
t1 = (-b-√Δ )/2a = (65-63)/16 = 1/8
t1 = (-b+√Δ )/2a = (65+63)/16 =128/16 = 16/2 =8
look : 8 = 2^3 and 1/8 = (2^-1)^3 and 1/2 =2^-1
but : 2^x =t ....(t > 0)
2^x = 2^3 ....x=3
2^x =(2^-1)^3 = 2^-3 ....... x= -3