Question

The number of solutions to the equation √x+5 + √5-x = 4 are.....
A)0
B)1
C)2
D)none of these

Answer 1

ANSWER

{c} 2

Step By Step Explanation

Here we have >

$\sqrt(x + 5) + \sqrt(5 - x) =4$

So we have

$x + 5 \geqslant 0$

=>$x \geqslant -5$ -------(i)

Also,

$x - 5 \geqslant 0$

=>$x \geqslant 5$ ----------(ii)

Now, On squaring both sides of $\sqrt(x + 5) + \sqrt(5 - x) =4$ we get =>

(x + 5) + (5 - x) +$2\sqrt(x + 5)\times \sqrt (5 - x)$ = 16

=> 10 + $2\sqrt( 5^{2} -x^{2})$ = 16

{By using (a+b)(a-b) = a² - b²}

=> $2\sqrt( 5^{2} - x^{2})$ = 16 - 10

=> $\sqrt(5^{2} - x^{2} )$ = $\dfrac6}{2}$

=> $\sqrt(5^{2} - x^{2})$ = 3

Now on squaring both sides we have >

=> 25 - x² =9

=> x² = 16

=> x =$\pm \sqrt 16$

=>x = $\pm 4$

Hence the number of solutions available for the equation are 2.

Answer 2

$\huge\bf{Answer:-}$

Yes

Step-by-step explanation:

Refer the attachment.