Let α,β∈R . If α,β2 are the roots of quadratic equation x2-px+1=0 and α2,β are the roots of quadratic equation x2-qx+8=0, then the value of 'r' if r8 is the arthemetic mean of p and q, is
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answer is 0083.00.
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Detailed Solution
αβ2=1,α2β=8αβ2α2β=8αβ=2 ⇒sub in αβ2=1 ⇒2β=1 We get α=4,β=12p=α+β2=4+14=174q=α2+β=16+12=332∴r8=p+q2r=4p+q=4174+332=17+66=83