Question

If( x-3)squared =16 find the positive value of x​

Answer 1

x=7, -1 so the positive value is 7

Explanation:

Answer 2

`\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 7}}}}}}`

`\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}`

`\: ({x - 3})^(2) = 16`

➺
`\: (x - 3) = √(16)`

➺
`\: (x - 3) = √(4 * 4)`

➺
`\: (x - 3) = \sqrt{( {4})^(2) }`

➺
`\: (x - 3) = ±4`

When
`x\:=\:+4`, we have

➺
`\: x = 4 + 3`

➺
`\boxed{x\:=\:7}`

When
`x\:=\:-4`, we have

➺
`\:(x - 3) = - 4`

➺
`\: x = - 4 + 3`

➺
`\boxed{x\:=\:-1}`

Therefore, the two values of
`x` are 7 and -1.

Hence, 7 is the positive value of
`x`.

`\sf \bf {\boxed {\mathbb {To\:verify:}}}`

➼
`\: ( {x - 3})^(2) = 16`

When
`x\:=\:7`

➼
`\: ({7 - 3)}^(2) = 16`

➼
`\: {4}^(2) = 16`

➼
`\: 16 = 16`

➼
`\: L.H.S.=R. H. S`

When
`x\:=\:-1`

`\: ({x - 3})^(2) = 16`

➼
`\:( { - 1 - 3})^(2) = 16`

➼
`\: ({ - 4})^(2) = 16`

➼
`\: 16 = 16`

➼
`\: L.H.S.=R. H. S`

`\sf\purple{Hence\:verified. }` ✔

`\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{☂}}}}}`