Question

$\sqrt { x } + \sqrt { 5 + x } = \frac { 15 } { \sqrt { 5 + x } }$
can anyone find its value
show step by step please today is my maths exam
question from class 10 ​

Answer 1

$\small{\color{green}{\fbox{\textsf{\textbf{Answer}}}}}$

• Let the age of father be x years

• Let the age of one of his children be y years and age of other children be z years

• From given information,

x=2×(y+z)...(1)

After 20 years,

(x+20)=(y+20)+(z+20)...(2)

• Substituting value of (1) in (2), we get

2×(y+z) +20=y+z+40

2y+2z−y−z=40−20

y+z=20...(3)

• Substituting value of (3) in (1), we get

x=2×(20)

⇒x=40

$<marquee direction = "up"> Thank You$

$<marquee direction = "left"> ❤Mr Majnu❤$

Answer 2

$\sf{{\sqrt{x}} + {\sqrt{5+x}} = {\dfrac{15}{{\sqrt{15+x}}}}}$

$\boxed{\sf{Simplify ~ {\dfrac{15}{{\sqrt{15+x}}}} ⇒ {\dfrac{15{\sqrt{15+x}}}{15+x}}}}$

$\sf{{\sqrt{x} + {\sqrt{5+x}} = {\dfrac{15{\sqrt{15+x}}}{15+x}}}}$

multiply both sides by 15 + x

$\sf{{\sqrt x}~(15+x) + {\sqrt{5+x}}~(15+x) = {\dfrac{15{\sqrt{15+x}}}{15+x}}~(15+x)}$

$\boxed{\sf{simplify~{\dfrac{15{\sqrt{15+x}}}{15+x}} ~(15+x) ⇒ 15{\sqrt{15+x}}}}$

${\sf{\sqrt{x}} ~(15+x) + {\sqrt{5+x}}~(15+x) = 15{\sqrt{15+x}}}$

$\boxed{\sf{solve~{\sqrt{x}} (15+x) + {\sqrt{5+x}}~(15+x)= 15 {\sqrt{15+x}} ⇒ x = {\dfrac{18{\sqrt{15}}}{7}}-{\dfrac{60}{7}}}}$

$\sf{\underline{\underline{x={\dfrac{18{\sqrt{15}}}{7}} -{\dfrac{60}{7}}}}}$