Question

How do you solve `\sqrt { 7u + 6} = \sqrt { 5u + 16}`?

Answer 1

`u=5`

Refer to the explanation for the process.

Explanation:

Solve:

`sqrt(7u+6)=sqrt(5u+16)`

Square both sides.

`(sqrt(7u+6))^2=(sqrt(5u+16))^2`

`7u+6=5u+16`

Subtract `5u` from both sides.

`7u-5u+6=5u-5u+16`

Simplify.

`2u+6=0+16`

`2u+6=16`

Subtract `6` from both sides.

`2u+6-6=16-6`

Simplify.

`2u+0=10`

`2u=10`

Divide both sides by `2`.

`(color(red)cancel(color(black)(2))^1u)/color(red)cancel(color(black)(2))^1=color(red)cancel(color(black)(10))^5/color(red)cancel(color(black)(2))^1`

Simplify.

`u=5`

Answer 2

`u=5`

Explanation:

`rarrsqrt(7u+6)=sqrt(5u+16)`

`rarr(sqrt(7u+6))^2=(sqrt(5u+16))^2`

`rarr7u+6=5u+16`

`rarr2u=10`

`rarru=5`