Question

x^2-16 under root x =12, x-2under root x=❓

Answer 1

The answer is 2

GIVEN

x² - 16√x = 12

TO FIND

The value of

x-2√x

SOLUTION

We can simply solve the above problem as follows;

We are given an expression,

x² - 16√x = 12

Bringing 12 in RHS;

x² - 16√x - 12 =

Squaring x and √x

x⁴- 16x- 12 = 0

Factoring the above equation;

(x² - 2x - 2)(x² + 2x + 6) = 0

$x = \frac{2 + \sqrt{4 - 4( - 2) } }{2}$

x = 1 + √3

x = 1 - √3

The positive root does not solve the orignal equation;

√x = 1 + √3

x = 4 + 2√3

Solving for,

x-2√x = 4 + 2√3 - 2(1+√3)

= 2

Hence, The answer is 2

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Answer 2

Answer: The answer is 2

Step-by-step explanation:

⇒$x^{2} -16\sqrt{x} =12$,x>0

transfer the 12 from LHS to RHS

⇒$x^{2} -16\sqrt{x} -12=0$

factorise the above equation,

⇒$(x-2\sqrt{x} -2)(x+2\sqrt{x} +6)=0$

since x>0

⇒$x-2\sqrt{x} -2=0$

⇒$x-2\sqrt{x} =2$

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