Algebra 2 questions. 10 points to best answer?

Question

6.)[SQRT(x + 3)] = 2[SQRT(x)]
A. no real solution
B. 3
C. {-3,3}
D. 0
E. 3/2
F. 1

7. [SQRT(2x2 + x - 12)] = x
A [SQRT(6)]
B. 3
C. no solution
D. [SQRT(12)]
E. 2
F. {-2,2}

8. 2[SQRT(x + 4)] = 3
A. -7/4
B. 1/2
C.-5/2
D. [SQRT(7/2)]
E. [SQRT(-7/2)]
F. none of the above

Answer 1

1) Given that

Squaring on bothsides

( x + 3) = 4x

4x - x - 3 = 0

3x - 3 = 0

3(x - 1) = 0

x - 1 = 0

x = 1

The answer is option ( F )

2 ) Given that

Squaring on bothsides

It can be solved in quadratic form

Here a = 1 , b = 1 , c = -12

Hence there is no solution

Therefore the answer is option ( C )

3 ) Given that

Squaring on bothsides

Therefore the answer is option ( A )

 

 

Comments

7).

x² + x - 12 = 0.

By factoring by grouping.

x² + 4x - 3x - 12 = 0

x(x + 4) - 3(x + 4) = 0

Factor : (x + 4)(x - 3) = 0.

Apply zero product property.

x + 4 = 0  and  x - 3 = 0

⇒ x = - 4  and  x = 3.

option B is the correct choice.