The number of integral solutions of the equations - x2-10x-21-x2-12x-32 - x2-10x-21-x2-12x-32 isare

The correct option is D No solutionGiven: equation |x^2 10x 21x^2 12x+32|= (x^2 10x+21x^2 12x+32) To find the number of integral solutions of the equation ...

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Standard XII

Mathematics

Multinomial Theorem

The number of...

Question

The number of integral solutions of the equations $∣ ∣ ∣ \frac{x^{2} - 10 x - 21}{x^{2} - 12 x + 32} ∣ ∣ ∣ = - (\frac{x^{2} - 10 x + 21}{x^{2} - 12 x + 32})$ is(are)

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Solution

The correct option is D No solution
Given: equation $∣ ∣ ∣ \frac{x^{2} - 10 x - 21}{x^{2} - 12 x + 32} ∣ ∣ ∣ = - (\frac{x^{2} - 10 x + 21}{x^{2} - 12 x + 32})$
To find the number of integral solutions of the equation
Sol: The given equation's absolute part has two parts.
Part 1: $+ (\frac{x^{2} - 10 x - 21}{x^{2} - 12 x + 32}) = - (\frac{x^{2} - 10 x + 21}{x^{2} - 12 x + 32}) ⟹ x^{2} - 10 x - 21 = - (x^{2} - 10 x + 21) ⟹ 2 x^{2} - 20 x = 0 ⟹ x = 10$
On back substituting we get no solution.
Part 2: $- (\frac{x^{2} - 10 x - 21}{x^{2} - 12 x + 32}) = - (\frac{x^{2} - 10 x + 21}{x^{2} - 12 x + 32})$
This gives no solution for $x$
Hence the number of integral solutions of the given equation is 0

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The number of integral solutions of the equations ∣∣∣x2−10x−21x2−12x+32∣∣∣=−(x2−10x+21x2−12x+32) is(are)

The number of integral solutions of the equations $∣ ∣ ∣ \frac{x^{2} - 10 x - 21}{x^{2} - 12 x + 32} ∣ ∣ ∣ = - (\frac{x^{2} - 10 x + 21}{x^{2} - 12 x + 32})$ is(are)