Question

Solve each equation below. Show your work!

Problem one :x² = 169
Problem two :x³ = −125
You REALLY need to show your work please!

Answer 1

Problem one:

`{ \tt{ {x}^(2) = 169 }}`

but 169 = 13², therefore:

`{ \tt{ {x}^(2) = {13}^(2) }}`

• apply square roots on all sides:

`{ \tt{ \sqrt{ {x}^(2) } = \sqrt{ {13}^(2) } }} \\ \\ { \boxed{ \boxed{ \: \: x = 13 \: \: }}}`

Problem two:

`{ \tt{ {x}^(3) = - 125}}`

but -125 = -5³, therefore:

`{ \tt{ {x}^(3) = - {5}^(3) }}`

• Apply cube roots to all sides:

`{ \tt{ \sqrt[3]{ {x}^(3) } = \sqrt[3]{ - 5 {}^(3) } }} \\ \\ { \boxed{ \boxed{ \tt{ \: \: x = - 5 \: }}}}`