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Given that g(x)=3x-7
Find the value of k
[tex]g^{2} (4k/3)=8[/tex]

Sagot :

xenia168

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]

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