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Algebra and Applications Test 2

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Question : 6 of 40

Marks: +1, -0

If

x^2 + 1 = 2x

, then the value of

\frac{x^4 + \frac{1}{x^2}}{x^2 - 3x + 1}

is:

0
1
2
-2

Solution: 👈: Video Solution

Concept:

Solve the given equation for

x

, then substitute it into the expression.

Explanation:

Given:

x^2 + 1 = 2x

.

Rearrange:

x^2 - 2x + 1 = 0

.

Factorise:

(x - 1)^2 = 0

.

So,

x - 1 = 0

and hence

x = 1

.

Now numerator:

x^4 + \frac{1}{x^2} = 1^4 + \frac{1}{1^2} = 1 + 1 = 2

.

Denominator:

x^2 - 3x + 1 = 1^2 - 3(1) + 1 = 1 - 3 + 1 = -1

.

Therefore, value

= \frac{2}{-1} = -2

.

Answer:

-2

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