x squared

Algebra Level 1

If x y = 100 xy = 100 , x z = 1000 xz = 1000 and y z = 10000 yz = 10000 , then what is x 2 x^2 ?


The answer is 10.

Erik Tang by Erik Tang , 17, USA

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2 solutions

Chew-Seong Cheong
Jul 27, 2018

x y × x z y z = 100 × 1000 10000 x 2 = 10 \begin{aligned} \frac {xy\times \color{#3D99F6} xz}{\color{#D61F06}yz} &= \frac {100 \times \color{#3D99F6} 1000}{\color{#D61F06}10000} \\ x^2 & = \boxed{10} \end{aligned}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
X X
Jul 27, 2018

Multiply the three equations and get ( x y z ) 2 = 1 0 9 (xyz)^2=10^9 ,square the third equation and get ( y z ) 2 = 1 0 8 (yz)^2=10^8 ,so x 2 = 1 0 1 = 10 x^2=10^1=10

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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