Being radical part 2/5

Algebra Level 1

What is the sum of the solutions to this equation: x 4 8 x 2 + 16 = 0 \sqrt { { x }^{ 4 }-8{ x }^{ 2 }+16 } =0


The answer is 0.

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1 solution

x 4 8 x 2 + 16 = 0 \sqrt { { x }^{ 4 }-8{ x }^{ 2 }+16 } =0
Let x 2 x^2 = = y y .
y 2 8 y + 16 = 0 \sqrt { { y }^{ 2 }-8y+16 } =0
y 2 4 y 4 y + 16 = 0 \sqrt{y^2-4y-4y+16}=0
( y 4 ) ( y 4 ) = 0 \sqrt{(y-4)(y-4)}=0
( y 4 ) = 0 (y-4)=0
y = 4 y=4
x 2 = 4 x^2=4
x = ± 2 \therefore x=\pm2
Now, their sum becomes, 2 + ( 2 ) = 0 2+(-2)=\boxed{0}


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