Just for fun

Algebra Level 1

If x 2 = 16 x^2=16 , then x 3 x^3 can be:

I. 64

II. -64

Both I and II I only Neither I nor II II only

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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3 solutions

Nihar Mahajan
Sep 5, 2015

x 2 = 16 ⇒ x 2 − 16 = 0 ⇒ ( x + 4 ) ( x − 4 ) = 0 x^2=16 \Rightarrow x^2-16=0 \Rightarrow (x+4)(x-4)=0

Case 1: x + 4 = 0 ⇒ x = − 4 ⇒ x 3 = ( − 4 ) 3 = − 64 x+4=0 \Rightarrow x=-4 \Rightarrow x^3=(-4)^3=\boxed{-64}

Case 2: x − 4 = 0 ⇒ x = 4 ⇒ x 3 = ( 4 ) 3 = 64 x-4=0 \Rightarrow x=4 \Rightarrow x^3=(4)^3=\boxed{64}

Thus I , I I I,II both are possible considering all cases.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Good solution.Up voted.

Sai Ram - 5 years, 9 months ago

What I don't get is that the answer is suppose to be a positive always, because when you have an exponent the anwser is basically going to be a positive because when having an exponent is basically just multiplying the same number .. In that case when multiplying the same integer always get you to a positive , no negative.. #confused

Ervin Cunanan - 5 years, 8 months ago

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That is only true of even exponents. A triple negative is a negative.

-4 x -4 = 16 x -4 = -64

Marc Brothers - 5 years, 7 months ago
Mohammad Khaza
Sep 30, 2017

x = + 4 , x = − 4 x=+4 ,x=-4

then, x 2 = 16 x^2=16

but x 3 = + 64 , − 64 x^3=+64,-64

1 Helpful 0 Interesting 0 Brilliant 0 Confused

x 2 = 16 x^2=16 ⇒ x = 4 , x = − 4 \Rightarrow x=4, x=-4 Then, 4 3 = 64 , ( − 4 ) 3 = − 64 4^3=\boxed{64}, (-4)^3=\boxed{-64}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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