What is sqrt((3-3x^2)^2+(6x)^2) ?

The solution to sqrt((3-3x^2)^2+(6x)^2) is 3x^2+3

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simplify sqrt((3-3x^2)^2+(6x)^2)

simplify

(3 - 3 x^{2})^{2} + (6 x)^{2}

3 x^{2} + 3

Solution steps

(3 - 3 x^{2})^{2} + (6 x)^{2}

Simplify

(3 - 3 x^{2})^{2} + (6 x)^{2} : 9 x^{4} + 18 x^{2} + 9

= 9 x^{4} + 18 x^{2} + 9

Factor out common term

9 : 9 (x^{4} + 2 x^{2} + 1)

= 9 (x^{4} + 2 x^{2} + 1)

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

9 (x^{4} + 2 x^{2} + 1) = 9 x^{4} + 2 x^{2} + 1

= 9 x^{4} + 2 x^{2} + 1

9 = 3

= 3 x^{4} + 2 x^{2} + 1

Simplify

x^{4} + 2 x^{2} + 1 : x^{2} + 1

= 3 (x^{2} + 1)

Expand

3 (x^{2} + 1) : 3 x^{2} + 3

= 3 x^{2} + 3

65 \times 5

65 \times 4

\frac{- 9}{4}

l im f (x)

What is sqrt((3-3x^2)^2+(6x)^2) ?
The solution to sqrt((3-3x^2)^2+(6x)^2) is 3x^2+3