What is the answer to 5sqrt(3/x)+7sqrt(x/3)= 222/3 ?

The answer to 5sqrt(3/x)+7sqrt(x/3)= 222/3 is x=330.96571…,x=0.01387…

Solve for x: 5sqrt(3/x)+7sqrt(x/3)= 222/3

The solution is x=330.96571…,x=0.01387…

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5 \frac{3}{x} + 7 \frac{x}{3} = \frac{222}{3}

x = 330.96571 \dots, x = 0.01387 \dots

Solution steps

5 \frac{3}{x} + 7 \frac{x}{3} = \frac{222}{3}

Rewrite the equation with

\frac{3}{x} = u

and

x = \frac{3}{u ^{2}}

5 u + 7 \frac{( \frac{3}{u ^{2}} )}{3} = \frac{222}{3}

Solve

5 u + 7 \frac{( \frac{3}{u ^{2}} )}{3} = \frac{222}{3} : u \approx 0.09520 \dots, u \approx - 0.09399 \dots, u \approx 14.70479 \dots

u \approx 0.09520 \dots, u \approx - 0.09399 \dots, u \approx 14.70479 \dots

Substitute back

u = \frac{3}{x},

solve for

x

Solve

\frac{3}{x} = 0.09520 \dots : x = 330.96571 \dots

Solve

\frac{3}{x} = - 0.09399 \dots :

No Solution for

x \in R

Solve

\frac{3}{x} = 14.70479 \dots : x = 0.01387 \dots

x = 330.96571 \dots, x = 0.01387 \dots

Verify Solutions:

x = 330.96571 \dots

True

, x = 0.01387 \dots

True

The solutions are

x = 330.96571 \dots, x = 0.01387 \dots

a = (3.631 x 1 0^{- 23})^{\frac{1}{3}}

\frac{x}{( 1 + x )} + \frac{( 1 + x )}{x} = \frac{5}{2}

36 = x^{\frac{2}{3}}

\frac{x}{3} = 15

x - 1 = 12

What is the answer to 5sqrt(3/x)+7sqrt(x/3)= 222/3 ?
The answer to 5sqrt(3/x)+7sqrt(x/3)= 222/3 is x=330.96571…,x=0.01387…
Solve for x: 5sqrt(3/x)+7sqrt(x/3)= 222/3
The solution is x=330.96571…,x=0.01387…