Question

Two equations are shown.



x
2
=
10

x
3
=
10



Which statements are TRUE about the solutions to these equations?

A.
The equation
x
2
=
10
has only one solution,
√
10
.

The equation
x
3
=
10
has only one solution,
3
√
10
.

B.
The equation
x
2
=
10
has only one solution,
√
10
.

The equation
x
3
=
10
has two solutions,
−
3
√
10
and
3
√
10
.

C.
The equation
x
2
=
10
has two solutions,
−
√
10
and
√
10
.

The equation
x
3
=
10
has only one solution,
3
√
10
.

D.
The equation
x
2
=
10
has two solutions,
−
√
10
and
√
10
.

The equation
x
3
=
10
has two solutions,
−
3
√
10
and
3
√
10
.

Answer 1

C

Reason: x^2 = 10 gives x = ±√10 (two real solutions). x^3 = 10 has the single real solution x = ∛10 (the other two cube roots are nonreal complex numbers), so only ∛10 is a real solution.