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The-number-of-real-solutions-of-the-equation-9-10-x-3-x-x-2-is-




Question Number 62612 by hovea cw last updated on 23/Jun/19
The number of real solutions of the  equation ((9/(10)))^x = −3+x−x^2      is
Thenumberofrealsolutionsoftheequation(910)x=3+xx2is
Answered by tanmay last updated on 23/Jun/19
−3+x−x^2   =−x^2 +x−3  =−(x^2 −x+3)  =−(x^2 −2×x×(1/2)+(1/4)−(1/4)+3)  =−(x−(1/2))^2 +(1/4)−3  =−(x−(1/2))^2 −((11)/4)<0 [always −ve]  but ((9/(10)))^x >0 [aleays +ve]  so no real solution
3+xx2=x2+x3=(x2x+3)=(x22×x×12+1414+3)=(x12)2+143=(x12)2114<0[alwaysve]but(910)x>0[aleays+ve]sonorealsolution

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