It is, or it isn't?

Algebra Level 2

If y 2 − 10 y = x 2 − 10 x , y^2 -10y = x^2 - 10x, , then does it necessarily follow that y = x y = x ?

No Yes

Vinayak Srivastava by Vinayak Srivastava , 15, India

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2 solutions

Rearranging the terms, we get

x 2 − y 2 − 10 x + 10 y = 0 x^2 - y^2 - 10x + 10y =0

( x − y ) ( x + y ) − 10 ( x − y ) = 0 (x-y)(x+y) - 10(x-y)=0

( x − y ) ( x + y − 10 ) = 0 (x-y)(x+y-10)=0

So, it may be either

x = y x = y

Or

x + y = 10 x + y = 10

5 Helpful 2 Interesting 1 Brilliant 0 Confused

What grade math is this?

Joyce Wong - 1 year ago

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Not specifically any grade but to solve it you will need a basic idea of Algebra I and II, which is basically 9th and 10th grade in India.

Kumudesh Ghosh - 1 year ago

The given equation is equivalent to

( x − 5 ) 2 = ( y − 5 ) 2 ⟹ x − 5 = ± ( y − 5 ) ⟹ x = y ∪ x + y = 10 (x-5)^2=(y-5)^2\implies x-5=\pm (y-5)\implies x=y\cup x+y=10 .

1 Helpful 0 Interesting 1 Brilliant 0 Confused

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