Number of values of x- satisfying the equation - x -8-2 - x -7- x -1- x -7-4A- 0B- 1C- 2D- 3

The correct option is B 1(√(x+7) + 1) + √((x+1) √(x+7)) = 4 nbsp; ⇒√((x+1) √(x+7)) = 3 √(x+7) ⇒ (x+1) √(x+7) = 9+(x+7) 6√(x+7) ⇒ 5√(x+7) = 15 ⇒ x + ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

Number of val...

Question

Number of values of $x$ , satisfying the equation $\sqrt{(x + 8) + 2 \sqrt{(x + 7)}} + \sqrt{(x + 1) - \sqrt{x + 7}} = 4,$ is

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Solution

The correct option is B $1$
$(\sqrt{x + 7} + 1) + \sqrt{(x + 1) - \sqrt{x + 7}} = 4$
$\Rightarrow \sqrt{(x + 1) - \sqrt{x + 7}} = 3 - \sqrt{x + 7}$
$\Rightarrow (x + 1) - \sqrt{x + 7} = 9 + (x + 7) - 6 \sqrt{x + 7}$
$\Rightarrow 5 \sqrt{x + 7} = 15$
$\Rightarrow x + 7 = 9 \Rightarrow x = 2$
Only one value of $x$ will satisfy the equation.

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Number of values of x, satisfying the equation √(x+8)+2√(x+7)+√(x+1)−√x+7=4, is

The correct option is B 1(√x+7+1)+√(x+1)−√x+7=4 ⇒√(x+1)−√x+7=3−√x+7 ⇒(x+1)−√x+7=9+(x+7)−6√x+7 ⇒5√x+7=15 ⇒x+7=9⇒x=2 Only one value of x will satisfy the equation.

Number of values of $x$ , satisfying the equation $\sqrt{(x + 8) + 2 \sqrt{(x + 7)}} + \sqrt{(x + 1) - \sqrt{x + 7}} = 4,$ is