Please Show Your Complete Solution:))), Pleaseeeee

Please Show your complete solution:)))
PLEASEEEEE

 

Answer:

1.

3 {t}^{2} = 12

3 {t}^{2} \div 3 = 12 \div 3

{t}^{2} = 4

t = \binom{ + }{ - } \sqrt{4}

t = \binom{ + }{ - } 2

t = - 2 \\ t = 2

checking:

3 {t}^{2} = 12

t = - 2

3( - 2)^{2} = 12

3(4) = 12

12 = 12

t = 2

3(2)^{2} = 12

3(4) = 12

12 = 12

2.

{x}^{2} - 7 = 0

{x}^{2} = 7

x = \binom{ + }{ - } \sqrt{7}

x = - \sqrt{7} \\ x = \sqrt{7}

Checking:

{x}^{2} - 7 = 0

x = - \sqrt{7}

( - \sqrt{7} )^{2} - 7 = 0

\sqrt{7}^{2} - 7 = 0

7 - 7 = 0

0 = 0

x = \sqrt{7}

( \sqrt{7})^{2} - 7 = 0

\sqrt{7}^{2} - 7 = 0

7 - 7 = 0

0 = 0

3.

3 {r}^{2} = 18

3 {r}^{2} \div 3 = 18 \div 3

{r}^{2} = 6

r = \binom{ + }{ - } \sqrt{6}

r = - \sqrt{6} \\ r = \sqrt{6}

checking:

3 {r}^{2} = 18

r = - \sqrt{6}

3( - \sqrt{6} )^{2} = 18

3 \times \sqrt{6}^{2} = 18

3 \times 6 = 18

18 = 18

r = \sqrt{6}

3( \sqrt{6} )^{2} = 18

3 \times \sqrt{6}^{2} = 18

3 \times 6 = 18

18 = 18

4.

{x}^{2} = 150

x = \binom{ + }{ - } 150

x = \binom{ + }{ - } \sqrt{ {5}^{2} \times 6}

x = \binom{ + }{ - } \sqrt{ {5}^{2} } \sqrt{6}

x = \binom{ + }{ - } 5 \sqrt{6}

x = - 5 \sqrt{6} \\ x = 5 \sqrt{6}

checking:

{x}^{2} = 150

x = - 5 \sqrt{6}

( - 5 \sqrt{6} )^{2} = 150

(5 \sqrt{6} )^{2} = 150

{5}^{2} \times \sqrt{6}^{2} = 150

25 \times 6 = 150

150 = 150

(5 \sqrt{6} )^{2} = 150

{5}^{2} \times \sqrt{6}^{2} = 120

25 \times 6 = 150

150 = 150

5.

{x}^{2} = \frac{9}{16}

x = \binom{ + }{ - } \sqrt{ \frac{9}{16} }

x = \binom{ + }{ - } \frac{3}{4}

x = - \frac{3}{4} \\ x = \frac{3}{4}

checking:

{x}^{2} = \frac{9}{16}

x = - \frac{3}{4}

( - \frac{3}{4} )^{2} = \frac{9}{16}

( \frac{3}{4} )^{2} = ( \frac{3}{4})^{2}

2 = 2

x = \frac{3}{4}

( \frac{3}{4} )^{2} = \frac{9}{16}

( \frac{3}{4} )^{2} = ( \frac{3}{4} )^{2}

2 = 2

6.

(s - 4)^{2} - 81 = 0

{s}^{2} - 8s + 16 - 81 = 0

{s}^{2} + 5s - 13s - 65 = 0

s \times (s + 5) - 13(s + 5) = 0

(s + 5) \times ( s - 13) = 0

s + 5 = 0 \\ s - 13 = 0

s = - 5 \\ s = 13

checking:

(s - 4)^{2} - 81 = 0

s = - 5

( - 5 - 4)^{2} - 81 = 0

( - 9)^{2} - 81 = 0

81 - 81 = 0

0 = 0

s = 13

(13 - 4)^{2} - 81 = 0

(9)^{2} - 81 = 0

81 - 81 = 0

0 = 0


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