Question

Given that g(x)=3x-7 Find the value of k la1" title="g^{2} (4k/3)=8" alt="g^{2} (4k/3)=8" align="absmiddle" class="latex-formula">

Answer 1

Answer:

{  $\frac{7}{4}$ - $\frac{\sqrt{2} }{2}$ ,  $\frac{7}{4}$ + $\frac{\sqrt{2} }{2}$ }

Step-by-step explanation:

ax² + bx + c = 0

$x_{12}$ = ( - b ± $\sqrt{b^2 -4ac}$ ) ÷ 2a

~~~~~~~~~~~

g(x) = 3x - 7

g²(x) = (3x - 7)²

g²(x) = 9x² - 42x + 49

g²( $\frac{4k}{3}$ ) = 9( $\frac{4k}{3}$ )² - 42( $\frac{4k}{3}$ ) + 49

9( $\frac{4k}{3}$ )² - 42( $\frac{4k}{3}$ ) + 49 = 8

16k² - 56k + 41 = 0

a = 16 , b = - 56 , c = 41

D = b² - 4ac = ( - 56)² - 4(16)(41) = 512 = $2^{9}$

$k_{1}$ = ( 56 + √$2^{9}$ ) ÷ 32 = $\frac{7}{4}$ + $\frac{\sqrt{2} }{2}$

$k_{2}$ = $\frac{7}{4}$ - $\frac{\sqrt{2} }{2}$