Solve 1/x^(-1/2)(7x 8)^(1/2) (7/2)*(1/2)(7x 8)^(-1/2)

Question

Simplify the expression

\frac{7}{4} x

Show Solution

x \in \emptyset

Evaluate

\frac{1}{x ^{- \frac{1}{2}}} \times (7 x \times 8)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (7 x \times 8)^{- \frac{1}{2}}

To find the roots of the expression,set the expression equal to 0

\frac{1}{x ^{- \frac{1}{2}}} \times (7 x \times 8)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (7 x \times 8)^{- \frac{1}{2}} = 0

Find the domain

More Steps

\frac{1}{x ^{- \frac{1}{2}}} \times (7 x \times 8)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (7 x \times 8)^{- \frac{1}{2}} = 0, x > 0

Calculate

\frac{1}{x ^{- \frac{1}{2}}} \times (7 x \times 8)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (7 x \times 8)^{- \frac{1}{2}} = 0

Multiply the terms

\frac{1}{x ^{- \frac{1}{2}}} \times (56 x)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (7 x \times 8)^{- \frac{1}{2}} = 0

Multiply the terms

\frac{1}{x ^{- \frac{1}{2}}} \times (56 x)^{\frac{1}{2}} (\frac{7}{2}) (\frac{1}{2}) (56 x)^{- \frac{1}{2}} = 0

Remove the unnecessary parentheses

\frac{1}{x ^{- \frac{1}{2}}} \times (56 x)^{\frac{1}{2}} \times \frac{7}{2} (\frac{1}{2}) (56 x)^{- \frac{1}{2}} = 0

Remove the unnecessary parentheses

\frac{1}{x ^{- \frac{1}{2}}} \times (56 x)^{\frac{1}{2}} \times \frac{7}{2} \times \frac{1}{2} (56 x)^{- \frac{1}{2}} = 0

Divide the terms

More Steps

x^{\frac{1}{2}} (56 x)^{\frac{1}{2}} \times \frac{7}{2} \times \frac{1}{2} (56 x)^{- \frac{1}{2}} = 0

Multiply

More Steps

\frac{7}{4} x^{\frac{1}{2}} = 0

Rewrite the expression

x^{\frac{1}{2}} = 0

The only way a root could be 0 is when the radicand equals 0

x = 0

Check if the solution is in the defined range

x = 0, x > 0

Solution

x \in \emptyset

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