The negative root of √(4x-18)+√(x+6) = √(2x+18)+√(3x-30) lies in the range of?
1)-1<x<1 5)-9<x<-7
2)-3<x<-1 6)-11<x<-9
3)-5<x<-3 7)-13<x<-11
4)-7<x<-5 8)-15<x<-13
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1)-1<x<1 5)-9<x<-7
2)-3<x<-1 6)-11<x<-9
3)-5<x<-3 7)-13<x<-11
4)-7<x<-5 8)-15<x<-13
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Verified answer
√(4x-18)+√(x+6) = √(2x+18)+√(3x-30)
√+√ = √+√
√(4x-18)+√(x+6) = √(2x+18)+√(3x-30)
Square both sides and:
(√(4x-18)+√(x+6) )²=(√(2x+18)+√(3x-30))²
4x-18 + 2√(4x-18)(x+6) + x+6 = 2x+18 + 2√(3x-30)(2x+18) + 3x-30
5x-12 +2√(4x²-18x+24x-108)=5x-12 + 2√(6x²-60x+54x-540)
2√(4x²-18x+24x-108)=2√(6x²-60x+54x-540)
4x²-18x+24x-108=6x²-60x+54x-540
4x²+6x-108=6x²-6x-540
-2x²+12x+432=0
Using the quadratic formula we find the roots 18 and -12.
Therefore answer 7