Question

Use the square root property to determine all real solutions for each of the following equations.3u2−24=0 u= 4r2+432=0 r= Give exact solutions (don't use decimals), and separate multiple solutions with commas. If there are no real solutions, type DNE.

Answer 1

Given:

`3u^2-24=0\text{ and }4r^2+432=0.`

Aim:

We need to find the values of u and r.

Step-by-step explanation:

`Consider\text{ }3u^2-24=0.`

Divide both sides of the equation by 3.

`\text{ }(3u^2)/(3)-(24)/(3)=(0)/(3).`

`u^2-8=0.`

Add 8 to thte both sides of the equation.

`u^2-8+8=0+8.`
`u^2=8`

Take sqaure root on both sides.

`√(u^2)=\pm√(8)`
`Use\text{ }√(u^2)=u\text{.}`

`u=\pm√(8)`

`u=\pm√(2*4)`

`u=\pm√(2*2^2)`

`u=\pm2√(2)`

`u=-2√(2),2√(2)`

`Consider\text{ }4r^2+432=0.`

Divide both sides of the equation by 4.

`(4r^2)/(4)+(432)/(4)=(0)/(4).`
`r^2+108=0`

Subtract 108 from both sides of the equation.

`r^2+108-108=0-108`
`r^2=-108`

Take square root on both sides of the equation.

`√(r^2)=\pm√(-108)`

`√(r^2)=\pm√((-1)*108)`
`We\text{ know that there is no real solution for }√((-1)).`

Final answer:

`u=-2√(2),2√(2)`
`r=DNE`