(C) Given equation: $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$. Let $f(x) = \sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} - (x + 5) = 0$. T

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(C) Given equation: $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$. Let $f(x) = \sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} - (x + 5) = 0$. Testing the options: For $x = 6$: $\sqrt{3(6)^2 - 7(6) - 30} + \sqrt{2(6)^2 - 7(6) - 5} = \sqrt{108 - 42 - 30} + \sqrt{72 - 42 - 5} = \sqrt{36} + \sqrt{25} = 6 + 5 = 11$. Right side: $x + 5 = 6 + 5 = 11$. Since $11 = 11$,$x = 6$ is the correct solution.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$,then $x = \dots$

A
$2$
B
$3$
C
$6$
D
$5$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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If $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$,then $x = \dots$

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