Question

helooo frnds....plzzz solve fast
if a and b are roots of quadratic equation x^2-2x+5=0 then form an equation whose roots are a^3+b^2-a+22 and b^3+4b^2-7b+35

Answer 1

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given equation x2−2x+3=0

⇒x=2±√22−4⋅1⋅32=1±√2i

Let α=1+√2iandβ=1−√2i

Now let

γ=α3−3α2+5α−2

⇒γ=α3−3α2+3α−1+2α−1

⇒γ=(α−1)3+α−1+α

⇒γ=(√2i)3+√2i+1+√2i

⇒γ=−2√2i+√2i+1+√2i=1

And let

δ=β3−β2+β+5

⇒δ=β2(β−1)+β+5

⇒δ=(1−√2i)2(−√2i)+1−√2i+5

⇒δ=(−1−2√2i)(−√2i)+1−√2i+5

⇒δ=√2i−4+1−√2i+5=2

So the quadratic equation having roots 

x2−(γ+δ)x+γδ=0

⇒x2−(1+2)x+1⋅2=0

⇒x2−3x+2=0

hope helps