If x_{1} and x_{2} are the solutions of the equation

Caitlyn Cole

Caitlyn Cole

Answered question

2022-04-21

If x1 and x2 are the solutions of the equation x2+pxap2=0, a=12+2 and pR{0}
Then prove that x14+x242

Answer & Explanation

Cristian Rosales

Cristian Rosales

Beginner2022-04-22Added 26 answers

Step 1
Note that
x14+x24=(x1+x2)44x13x26x12x224x1x22=
=(x1+x2)4x1x2(4x12+6x1x2+4x22)=
=(x1+x2)4x1x2(4(x1+x2)22x1x2
Then use the Vieta's formulae for x1+x2 and x1x2.
See if you can show that what you get is greater of equal to 2.

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