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Q. 79

Expert-verifiedFound in: Page 284

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Solve given equation and verify your result using graphing utility.

${e}^{{x}^{2}}={e}^{3x}.\frac{1}{{e}^{2}}$

The solution set is $\{1,2\}$ and it is verified through graph.

The given equation is :

${e}^{{x}^{2}}={e}^{3x}.\frac{1}{{e}^{2}}$

We have to solve for x and verify using graphing utility.

Using law of exponents , get a single expression with base e on right side .

${e}^{3x}.\frac{1}{{e}^{2}}={e}^{3x}.{e}^{-2}={e}^{3x-2}$

Since bases are same , therefore the exponential powers should also be the same.

${x}^{2}=3x-2\phantom{\rule{0ex}{0ex}}{x}^{2}-3x+2=0\phantom{\rule{0ex}{0ex}}$

Factorise above expression.

$(x-1)(x-2)=0\phantom{\rule{0ex}{0ex}}(x-1)=0,(x-2)=0\phantom{\rule{0ex}{0ex}}x=1,x=2\phantom{\rule{0ex}{0ex}}$

Graph

${Y}_{1}={e}^{{x}^{2}}\phantom{\rule{0ex}{0ex}}{Y}_{2}={e}^{3x-2}$

Determine the point of intersection.

The graph intersects at $x=1,x=2$

So the solution set is $\{1,2\}$.

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