Question

√(x/x+16)+√(x+16/x)=25/12


plz help me to solve the value of x.​

Answer 1

Answer:

the anwer of this equation is like 679

Answer 2

The value of x is 144/7 and -256/7.

We have to find the value of x for which

$\sqrt{\frac{x}{x+16}}+\sqrt{\frac{x+16}{x}}=\frac{25}{12}$

$\text{Let,}\sqrt{\frac{x}{x+16}}=t\implies\sqrt{\frac{x+16}{x}}=\frac{1}{t}$

Now,

$\implies t+\frac{1}{t}=\frac{25}{12}\\\\\implies\frac{t^2+1}{t}=\frac{25}{12}\\\\\implies12(t^2+1)=25t\\\\\implies12t^2+12-25t=0\\\\\implies12t^2-16t-9t+12=0\\\\\implies4t(3t-4)-3(3t-4)=0\\\\\implies(4t-3)(3t-4)=0\\\\\implies t=\frac{3}{4},\frac{4}{3}$

Now If we take, t = 3/4 ⇒ 1/t = 4/3

So, We can take any one of them, let's take, t = 3/4

$\implies\sqrt{\frac{x}{x+16}}=\frac{3}{4}\\\\\implies\frac{x}{x+16}=\frac{9}{16}\\\\\implies x=\frac{144}{7}$

Now we take, t = 4/3

$\implies\sqrt{\frac{x}{x+16}}=\frac{4}{3}\\\\\implies\frac{x}{x+16}=\frac{16}{9}\\\\\implies x=\frac{-256}{7}$

Therefore the value of x is 144/7 and -256/7.

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