Which value(s) of x satisfies the equation above?

AAPL wrote: ↑

Sat Feb 22, 2020 7:11 am

Magoosh

\(2x-2=\sqrt{3x^2+13}\)

Which value(s) of \(x\) satisfies the equation above?

I. \(-1\)
II. \(4\)
III. \(9\)

A. I
B. II
C. I and II
D. I and III
E. I, II, and III

OA B

Let’s substitute each value in the given equation:

I. x = -1

Is 2(-1) - 2 = √[(3(-1)^2 + 13]?

Is -2 - 2 = √(3 + 13)?

Is -4 = √16?

Is -4 = 4? No!

Statement I is not true.

II. x = 4

Is 2(4) - 2 = √(3*4^2 + 13)?

Is 6 = √(3*16 + 13)?

Is 6 = √(48 + 13)?

Is 6 = √61? No!

Statement II is not true.

III. x = 9

Is 2(9) - 2 = √(3*9^2 + 13)?

Is 18 - 2 = √(3*81 + 13)?

Is 16 = √(243 + 13)?

Is 16 = √256? Yes!

Statement III is true.

Answer: Only III