quadratic?

**decoy808** · February 10th 2010, 04:51 AM

two questons, are they both quadratic? if anyone could get me started much appreciated.

(a) $3{^2{^x}}+ 8 . 3{^x}-9=0$ (multiply 8 x 3x)

(b) $e{^2{^x}}+ 8e{^x}=3^2$

**Raoh** · February 10th 2010, 04:58 AM

Originally Posted by decoy808

two questons, are they both quadratic? if anyone could get me started much appreciated.

(a) $3{^2{^x}}+ 8 . 3{^x}-9=0$ (multiply 8 x 3x)

(b) $e{^2{^x}}+ 8e{^x}=3^2$

hi

you can put $3^x=X$ and see what happens.

**danielomalmsteen** · February 10th 2010, 05:05 AM

b)

define $e^x = u$ then the equation is equivalent to $u^2+8u-9=0$

Factoring

$(u+9)(u-1)=0$

solutions $u=1$ and $u=-9$

As the exponential negative values does not yield, the solution is

$u=1=e^x \rightarrow x=0$

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