Question

(2^x+2)^2=4^4 find the value of x

Answer 1

$(2 {x}^{2} + 2)^{2} = {4}^{4}$

$\implies \: (4x^{4} + 8x^{2}+4 )= {4}^{4}$

$\implies \: 4(x^{4} + 2x^{2}+1)= 4 ^{4}$

$\implies{x}^{4} + 2 {x}^{2}+1= \frac{4^{4} }{4}$

$\implies{x}^{4} + 2 {x}^{2}+1= {4}^{3}$

$\implies {x}^{4} + 2 {x}^{2} + 1 = 64$

$\implies{x}^{4} + 2 {x}^{2} + 1 - 64 = 0$

$\implies{x}^{4} + 2 {x}^{2} -63 = 0$

Hope its help u dear .