Solve the following equation- -2x - 6 - -x - 1 - 2

√( 2x+6 ) √( x+1 ) =2 squaring both sides, ⇒ 2x+6+x+1 2√( x+1 )√( 2x+6 ) =4 #160; #160; #160; #160; 3x+7 4=2√( x+1 )√( 2x+1 ) #160; ...

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Standard XII

Mathematics

Nature of Roots

Solve the fol...

Question

Solve the following equation:
$\sqrt{2 x + 6} - \sqrt{x + 1} = 2$

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Solution

$\sqrt{2 x + 6} - \sqrt{x + 1} = 2$
squaring both sides,
$\Rightarrow 2 x + 6 + x + 1 - 2 \sqrt{x + 1} \sqrt{2 x + 6} = 4$
$3 x + 7 - 4 = 2 \sqrt{x + 1} \sqrt{2 x + 1}$
${(3 x + 3)}^{2} = 4 (x + 1) (2 x + 1)$
$9 x^{2} + 9 + 18 x = 4 (2 x^{2} + x + 2 x + 1)$
$9 x^{2} + 18 x + 9 = 8 x^{2} + 12 x + 4$
$x^{2} + 6 x + 5 = 0$
$\Rightarrow x^{2} + x + 5 x + 5 = 0$
$\Rightarrow x (x + 1) + 5 (x + 1) = 0$
$\Rightarrow (x + 1) (x + 5) = 0$
$\Rightarrow x = - 1, - 5$
Hence, the answer is $- 1, - 5.$

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Solve the following equation:√2x+6−√x+1=2

√2x+6−√x+1=2squaring both sides,⇒2x+6+x+1−2√x+1√2x+6=4 3x+7−4=2√x+1√2x+1 (3x+3)2=4(x+1)(2x+1) 9x2+9+18x=4(2x2+x+2x+1) 9x2+18x+9=8x2+12x+4 x2+6x+5=0⇒x2+x+5x+5=0⇒x(x+1)+5(x+1)=0⇒(x+1)(x+5)=0⇒x=−1,−5Hence, the answer is −1,−5.

Solve the following equation:
$\sqrt{2 x + 6} - \sqrt{x + 1} = 2$