Question

What is the solution to the equation?

Answer 1

$\implies {\blue {\boxed {\boxed {\purple {\sf {A. \:-39}}}}}}$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}$

$\sqrt[5]{x + 7} = - 2$

➺$\: x + 7 =( { - 2})^{5}$

➺$\: x + 7 = ( - 2 \times - 2 \times - 2 \times - 2 \times - 2)$

➺$\: x + 7 = - 32$

➺$\: x = - 32 - 7$

➺$\: x = - 39$

$\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}$

$\sqrt[5]{x + 7} = - 2 \\\\ ➼ \: \sqrt[5]{ - 39 + 7} = - 2 \\ \\➼ \: \sqrt[5]{ - 32} = - 2 \\\\ ➼ \: \sqrt[5]{ - 2 \times - 2 \times - 2 \times - 2 \times - 2} = - 2\\ \\ ➼ \: \sqrt[5]{( { - 2})^{5} } = - 2\\ \\ ➼ \: - 2 = - 2 \\\\ ➼ \: L.H.S.=R. H. S$

Hence verified.

$\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning. }}{\orange{❦}}}}}$