S and G are roots of \(\displaystyle{x}^{{2}}-{3}{x}+{1}={0}\).

aanvarendbq28

aanvarendbq28

Answered question

2022-03-30

S and G are roots of x23x+1=0. Find equation whose roots are 1S2 and 1G2.

Answer & Explanation

Laylah Hebert

Laylah Hebert

Beginner2022-03-31Added 15 answers

Note SG=1,>S+G=3. Then
1S21G2=1SG2(S+G)+4=1
1S2+1G2=S+G4SG2(S+G)+4=1
Thus, the equation with roots 1S2 and 1G2 is
x2x1=0
pypberissootcu

pypberissootcu

Beginner2022-04-01Added 14 answers

The substitution method your teacher is referring to goes as follows:
Let y=1x2 where x=S, G are the roots of the given equation x23x+1=0
Rearranging gives x=1+2yy
Substituting this into the equation satisfied by x gives
(1+2yy)23(1+2yy)+1=0
This simplifies to become
y2y1=0
This is the same as the answer obtained by Quanto using Vieta's formulas.

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