Question

★ STANDARD QUESTION 6 ★

★ CONTENT QUALITY SUPPORT REQUIRED ★

Solve for " x "

$\sqrt{x {}^{2} - 7ax + 10 {a}^{2} } - \sqrt{x {}^{2} + ax - 6 {a}^{2} } = (x - 2a)$
★ LEVEL - 100 ★

Answer 1

mark it brain list,,,,,,,,, if you satisfied

Answer 2

Hey friend, Harish here.

Here is your answer:
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$\sqrt{ x^{2} - 7ax+10a^{2}} - \sqrt{ x^{2} +ax - 6a^{2}} =(x-2a)$

⇒ $\sqrt{ x^{2} - 2ax-5ax+10a^{2}} - \sqrt{ x^{2}-2ax+3ax-6a^{2}} = (x-2a)$

⇒$\sqrt{(x-5)(x-2a)} - \sqrt{(x+3a)(x-2a)}= (x-2a)$

⇒$( \sqrt{x -2a})[( \sqrt{x-5a} - \sqrt{x+3a})] = (x-2a)$

⇒$( \sqrt{x-5a} - \sqrt{x+3a}) = \sqrt {x-2a}$

Squaring on both sides, We get.

⇒$x-5a +x +3a -2 ( \sqrt{(x-5a)(x+3a})} = (x-2a)$

⇒$2 ( \sqrt{(x-5a)(x+3a})} = x$

⇒$4(x-5a)(x+3a}) = x^{2}$

⇒$3 x^{2} -8ax -60a^{2} = 0$

⇒$3 x^{2} -18ax +10ax -60a^{2} = 0$

⇒$3x(x - 6a) +10a(x -6a) = 0 \\ \\ (3x+10a)(x-6a) = 0$

Therefore the value of x is 6a or -10/3 a.
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