Question

solve the equation x 1⁄2-x 1⁄4-6=0

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER:

To Solve:

• $x^{\frac{1}{2}}-x^{\frac{1}{4}}-6=0$

Solution:

We are given that,

$\implies x^{\frac{1}{2}}-x^{\frac{1}{4}}-6=0$

$\implies x^{\frac{2}{4}}-x^{\frac{1}{4}}-6=0$

Let us assume that,

$\implies x^{\frac{1}{4}}=y$

So,

$\implies x^{\frac{2}{4}}=y^2$

Therefore,

$\implies x^{\frac{2}{4}}-x^{\frac{1}{4}}-6=0$

$\implies y^2-y-6=0$

Splitting the middle term,

$\implies y^2-3y+2y-6=0$

$\implies y(y-3)+2(y-3)=0$

$\implies(y-3)(y+2)=0$

So,

$\implies y=3,\:-2$

But,

$\implies x^{\frac{1}{4}}=y$

Case 2: Taking y = -2,

$\implies x^{\frac{1}{4}}=-2$

So,

$\implies x^{\frac{4}{4}}=(-2)^4$

$\implies x=16$

Therefore,

$\implies\bf x=16,81$