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how many real solution this eq. have (9/10)^x=-3+x-x^2

how many real solution this eq. have
(9/10)^x=-3+x-x^2

Grade:11

1 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-.6 cm}$Given $\bf{\left(\frac{9}{10}\right)^x = -3+x-x^2\Rightarrow \left(\frac{9}{10}\right)^x = -\left[x^2-x+3\right]}$\\\\\\So we get $\bf{\underbrace{\bf{\left(\frac{9}{10}\right)^x}}_{> 0}= \underbrace{\bf{-\left[\left(x-\frac{1}{4}\right)^2+\frac{11}{4}\right]}}_{<0}}$.\\\\\\So from above we get no real solution.

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