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Algebra Level 3

x 3 − 5 x 2 + 8 x − 4 x 2 − 3 x + 2 \frac{x^{3}-5x^{2}+8x-4}{x^{2}-3x+2} IF THE VALUE OF ABOVE EQUATION IS 1 THEN,

FIND ALL THE VALUES OF X

1 2 1,2,3 1,2 3

Sai Aryanreddy by sai aryanreddy , 28, India

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2 solutions

Kushagra Sahni
Nov 1, 2015

There was no need to solve, just observe that all the other 4 options contained 1,2 or both which isn't possible as the denominator then would be 0.

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Even I did the same ^_^

Akshat Sharda - 5 years, 7 months ago

We can factor the given equation as ( x − 1 ) ( x − 2 ) 2 ( x − 1 ) ( x − 2 ) = 1. \dfrac{(x - 1)(x - 2)^{2}}{(x - 1)(x - 2)} = 1.

Now for both x = 1 x = 1 and x = 2 x = 2 both the numerator and denominator equal 0 , 0, hence making the expression on the LHS indeterminate. Thus there are points of discontinuity for this expression at x = 1 , 2. x = 1,2.

For x ≠ 1 , 2 x \ne 1,2 we can cancel terms to obtain the simplified equation x − 2 = 1 ⟹ x = 3 . x - 2 = 1 \Longrightarrow \boxed{x = 3}.

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