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Question Number 167489 by mathlove last updated on 18/Mar/22

a+(√x)=2 b+(x)^(1/4) =9 ^( (4a−b^2 )=?)

a+x=2b+x4=9(4a−b2)=?

Answered by Rasheed.Sindhi last updated on 18/Mar/22

a+(√x)=2...(i) b+(x)^(1/4) =9...(ii) ^( (4a−b^2 )=?) (i)⇒(√x) =2−a..........(iii) (ii)⇒(x)^(1/4) =9−b⇒(√x) =(9−b)^2 ...(iv) (iii) & (iv):2−a=(9−b)^2 2−a=81+b^2 −18b a=−b^2 +18b−79 4a−b^2 =4(−b^2 +18b−79)−b^2 =−5b^2 +72b−316 b^2 −18b+a+79=0 b=((18±(√(18^2 −4a−316)))/2) =((18±2(√(2−a)))/2) =((18±2(√((9−b)^2 )))/2)=9±(9−b)=9±9∓b b±b=±18⇒b=9 b=9⇒a=−b^2 +18b−79=−9^2 +18∙9−79 =−160+162=2 4a−b^2 =4(2)−9^2 =8−81=−73

a+x=2...(i)b+x4=9...(ii)(4a−b2)=?(i)⇒x=2−a..........(iii)(ii)⇒x4=9−b⇒x=(9−b)2...(iv)(iii)&(iv):2−a=(9−b)22−a=81+b2−18ba=−b2+18b−794a−b2=4(−b2+18b−79)−b2=−5b2+72b−316b2−18b+a+79=0b=18±182−4a−3162=18±22−a2=18±2(9−b)22=9±(9−b)=9±9∓bb±b=±18⇒b=9b=9⇒a=−b2+18b−79=−92+18⋅9−79=−160+162=24a−b2=4(2)−92=8−81=−73

Commented by mathlove last updated on 18/Mar/22

thanks bro

thanksbro

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