Question

$\sqrt{3x + 10} + \sqrt{6 - x} = 6$
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Answer 1

Actual Question :

$\sqrt{3x + 10} + \sqrt{6 - x } = 6$

Let (3x + 10) be a

And (6 - x) be b

Squaring Both The Sides :

a + b + 2√(ab) = 36

3x + 10 + 6 - x + 2√{(3x + 10)(6 - x)} = 36

2x + 16 + 2√{18x - 3x² + 60 - 10x} = 36

x + 8 + √{8x - 3x² + 60} = 18

√{8x - 3x² + 60} = 10 - x

Again Squaring Both The Sides :

8x - 3x² + 60 = (10 - x)²

8x - 3x² + 60 = 100 + x² - 20x

4x² - 28x + 40 = 0

x² - 7x + 10 = 0

x² - 5x - 2x + 10 = 0

x(x - 5) -2(x - 5) = 0

(x - 5)(x - 2) = 0

Hence : x = 5 or x = 2