Question

Qual é o valor de :y = (1 + x}^ 4 + (1 - x}^4?

Answer 1

$\displaystyle \sf y = (1+x)^4+(1-x)^4 \\\\ \text{Fa{\c c}amos} : \\\\ y = [(1+x)^2]^2 +[(1-x)^2]^2 \\\\ y = [1+2x+x^2]^2 + [1-2x+x^2]^2 \\\\\ \text{Fa{\c c}amos} }:\\\\ 1+x^2 = m \\\\ y = [m+2x]^2+[m-2x]^2 \\\\ y = m^2+4x\cdot m+4x^2+m^2-4x\cdot m +4x^2 \\\\ y = 2m^2+8x^2\\\\ y = 2(1+x^2)^2+8x^2 \\\\ y = 2(1+2x^2+x^4)+8x^2 \\\\ y = 2x^4+4x^2+2 + 8x^2 \\\\ \huge\boxed{\sf \ y = 2x^4+12x^2+2 \ }\checkmark$