Answer:
Explanation:
From the question,
[tex]\frac{a^{3} - b^{3} }{(a - b)^{3} }[/tex] = [tex]\frac{73}{3}[/tex]
Let the equation be equal to zero.
[tex]\frac{a^{3} - b^{3} }{(a - b)^{3} }[/tex] - [tex]\frac{73}{3}[/tex] = 0
[tex]\frac{(a - b) *(a^{2} + ab + b^{2}) }{(a - b)^{3} }[/tex] - [tex]\frac{73}{3}[/tex] = 0
⇒ [tex]\frac{(a^{2} + ab + b^{2}) }{(a - b)^{2} }[/tex] - [tex]\frac{73}{3}[/tex] = 0
Find the LCM,
[tex]\frac{(a^{2} + ab + b^{2} )* 3 -73*(a - b)^{2} }{3*(a - b)^{2} }[/tex] = 0
[tex]\frac{-70a^{2} + 149ab -70b^{2}}{3*(a^{2} -2ab + b^{2}) }[/tex] = 0
Factorizing the numerator and denominator gives,
[tex]\frac{(10b - 7a)*(10a - 7b)}{3*(a - b)^{2} }[/tex] = 0
Multiply through by the denominator to have,
[tex]\frac{(10b - 7a)*(10a - 7b)}{3*(a - b)^{2} }[/tex] × 3*[tex](a - b)^{2}[/tex]= 0 × 3[tex](a - b)^{2}[/tex]
⇒ (10b - 7a)*(10a - 7b) = 0
∴ -7a + 10b = 0 or -7b + 10a =
These gives the equation of a straight line; y = mx + b
Solving these equations graphically, we have;
For -7b + 10a = 0,
m = 1.429
a-intercept = 0.00000
b-intercept = -0.00000
For -7a + 10b = 0,
m = 0.700
a-intercept = -0.00000
b-intercept = 0.00000
