ધારો કે S એ સમીકરણ 3^{x}left(3^{x}-1right)+2= | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let $3^{x}=t ; t>0$

$t(t-1)+2=|t-1|+|t-2|$

$t^{2}-t+2=|t-1|+|t-2|$

Case$-I $: $t<1$

$t^{2}-t+2=1-t+2-t$

$t^{2}+2=3-t$

$t^{2}+t

Vedclass · Accepted Answer

એકાકી ગણ

Vedclass · Answer

Let $3^{x}=t ; t>0$

$t(t-1)+2=|t-1|+|t-2|$

$t^{2}-t+2=|t-1|+|t-2|$

Case$-I $: $t<1$

$t^{2}-t+2=1-t+2-t$

$t^{2}+2=3-t$

$t^{2}+t-1=0$

$\mathrm{t}=\frac{-1 \pm \sqrt{5}}{2}$

$\mathrm{t}=\frac{\sqrt{5}-1}{2}$ is only acceptable

Case-II $: 1 \leq t<2$

$t^{2}-t+2=t-1+2-t$

$t^{2}-t+1=0$

$\mathrm{D}<0 $ no real solution

Case-III : $t \geq 2$

$t^{2}-t+2=t-1+t-2$

$\mathrm{t}^{2}-3 \mathrm{t} \quad 5=0 \Rightarrow \mathrm{D}<0$ no real solution

ધારો કે $S$ એ સમીકરણ $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| $ ના વાસ્તવિક બીજનો ગણ હોય તો $\mathrm{S}$ એ .. . .

Similar Questions

જો $\sqrt {3{x^2} - 7x - 30} + \sqrt {2{x^2} - 7x - 5} = x + 5,\,$ તો $\,\,{\rm{x = \ldots }}..{\rm{ }}$

જો $x_1,x_2,x_3 \in R-\{0\} $ ,$x_1 + x_2 + x_3\neq 0$ અને $\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}=\frac{1}{x_1+x_2+x_3}$, હોય તો $\frac{1}{{x^n}_1+{x^n}_2+{x^n}_3} =\frac{1}{{x^n}_1}+\frac{1}{{x^n}_2}+\frac{1}{{x^n}_3}$ .......... માટે શકય છે