Question

$3 {x}^{2} - 3 \sqrt{2}x + 1$
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Answer 1

Answer:

32

Step-by-step explanation:

32

α,β are the roots of x

2

−2x+4=0

⇒α+β=2,αβ=4

α

2

+β

2

=(α+β)

2

−2αβ

=2

2

−2(4)

=4−8=−4

α

3

+β

3

=(α+β)

3

−3αβ(α+β)

=2

3

−3(4)(2)

=8−24=−16

Now, α

5

+β

5

=(α

3

+β

3

)(α

2

+β

2

)−α

3

β

2

−α

2

β

3

=(α

3

+β

3

)(α

2

+β

2

)−(αβ)

2

(α+β)

=(−16)(−4)−(4)

2

(2)

=64−32=32

Answer 2

Answer:

$\tt \red{3x ^ { 2 } -3 \sqrt{ 2 } x+1=0}$

$\tt \pink{3x^{2}+\left(-3\sqrt{2}\right)x+1=0 }$

$\tt \pink{x=\frac{-\left(-3\sqrt{2}\right)±\sqrt{\left(-3\sqrt{2}\right)^{2}-4\times 3}}{2\times 3} }$

$\tt \red{x=\frac{-\left(-3\sqrt{2}\right)±\sqrt{18-4\times 3}}{2\times 3} }$

$\tt \purple{x=\frac{-\left(-3\sqrt{2}\right)±\sqrt{18-12}}{2\times 3} }$

$\tt \blue{x=\frac{3\sqrt{2}±\sqrt{6}}{6} }$

$\tt \purple{x=\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{6} }$

$\tt \blue{x=\frac{\sqrt{2}}{2}-\frac{\sqrt{6}}{6} }$

Answer:

Step-by-step explanation:

hope it help you.

thanks