Answer:
{ [tex]\frac{7}{4}[/tex] - [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{7}{4}[/tex] + [tex]\frac{\sqrt{2} }{2}[/tex] }
Step-by-step explanation:
ax² + bx + c = 0
[tex]x_{12}[/tex] = ( - b ± [tex]\sqrt{b^2 -4ac}[/tex] ) ÷ 2a
~~~~~~~~~~~
g(x) = 3x - 7
g²(x) = (3x - 7)²
g²(x) = 9x² - 42x + 49
g²( [tex]\frac{4k}{3}[/tex] ) = 9( [tex]\frac{4k}{3}[/tex] )² - 42( [tex]\frac{4k}{3}[/tex] ) + 49
9( [tex]\frac{4k}{3}[/tex] )² - 42( [tex]\frac{4k}{3}[/tex] ) + 49 = 8
16k² - 56k + 41 = 0
a = 16 , b = - 56 , c = 41
D = b² - 4ac = ( - 56)² - 4(16)(41) = 512 = [tex]2^{9}[/tex]
[tex]k_{1}[/tex] = ( 56 + √[tex]2^{9}[/tex] ) ÷ 32 = [tex]\frac{7}{4}[/tex] + [tex]\frac{\sqrt{2} }{2}[/tex]
[tex]k_{2}[/tex] = [tex]\frac{7}{4}[/tex] - [tex]\frac{\sqrt{2} }{2}[/tex]
