Question

Value of x satisfying
\sqrt{x + 3} + \sqrt{x - 2} = 5x+3​+x−2​=5 
is,​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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Here is Your Answer...!!

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Step by step solution:

THERE SHOULD NOT BE 5x+3​+x−2 TERMS

$Given \ \sqrt{x + 3} + \sqrt{x - 2} =5\\\\we \ have \ to \ find \ x\\\\we \ can \ write \ it \ as\\\\(x+3)^\frac{1}{2}+(x-2)^\frac{1}{2}=5\\\\ Power \ is \ same \ so \ formula \ here \ x^a+y^a=(xy)^a\\\\((x+3)(x-2))^\frac{1}{2}=5\\\\squaring \ on \ both \ side\\ \\we \ get\\\\(x+3)(x-2)=25\\\\x^{2}-2x+3x-6=25\\\\x^{2}+x-31=0$

$using \ formula\\\\x=\frac{-b+-\sqrt{b^2-4ac} }{2a}\\\\x^2+x-31=0\\\\x=\frac{-1+-\sqrt{1^2+4 \times31} }{2 \times1}\\ \\x=\frac{-1+-\sqrt{125} }{2}=\frac{-1+-5\sqrt{5} }{2}\\ \\so \ x=\frac{-1+5\sqrt{5} }{2} \ or \ x=\frac{-1-5\sqrt{5} }{2}$

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