Solve the following equation- -x - 3 - 1 - -x - -x - 2

Squaring on both sides 4 2√((x+3))= √((x 2)) Squaring on both sides #160; 16=4(x+3) (9x 2) 4√((x^2+x 6)) simplifying and squaring again 7x^2+16x 9 ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

Solve the fol...

Question

Solve the following equation:
$\sqrt{x + 3} - 1 = \sqrt{x - \sqrt{x - 2}}$

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Solution

Squaring on both sides
$4 - 2 \sqrt{(x + 3)} = - \sqrt{(x - 2)}$
Squaring on both sides
$16 = 4 (x + 3) - (9 x - 2) - 4 \sqrt{(x^{2} + x - 6)}$
simplifying and squaring again
$⟹ 7 x^{2} + 16 x - 96 = 0$
so $x = 2.73, - 5.10$ (approx)
By considering Domain
$x = 2.73$

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Solve the following equation:√x+3−1=√x−√x−2

Squaring on both sides4−2√(x+3)=−√(x−2)Squaring on both sides 16=4(x+3)−(9x−2)−4√(x2+x−6)simplifying and squaring again⟹7x2+16x−96=0so x=2.73,−5.10 (approx)By considering Domainx=2.73

Solve the following equation:
$\sqrt{x + 3} - 1 = \sqrt{x - \sqrt{x - 2}}$

Squaring on both sides
$4 - 2 \sqrt{(x + 3)} = - \sqrt{(x - 2)}$
Squaring on both sides
$16 = 4 (x + 3) - (9 x - 2) - 4 \sqrt{(x^{2} + x - 6)}$
simplifying and squaring again
$⟹ 7 x^{2} + 16 x - 96 = 0$
so $x = 2.73, - 5.10$ (approx)
By considering Domain
$x = 2.73$