Question

if a and b are the roots of the equation 5x² - 3x -2 =0 find the value of a³ + b³​

Answer 1

$\huge \orange{ \overbrace{ \red{\underbrace \color{blue} {\underbrace \color{black}{\colorbox{lime}{ {\red \: {☘Answer ☘ }}}}}}}}$

✪QUESTION✪:-

if a and b are the roots of the equation 5x² - 3x -2 =0 find the value of a³ + b³

✪ANSWER✪:-

$\boxed{\sf{ 5x² - 3x -2 = 0}}$

it is in the form of px² + qx + r = 0

here ,

• p = 5
• q = -3
• r = -2

➠sum of the roots = a + b = -q/p

➠a + b = -(-3)/5

➠a + b = 3/5 ➜(1)

➠a = 3/5 - b ➜(2)

➠Product of roots = ab = r/p

➠ab = -2/5

➠(3/5 - b) b = -2/5 [from (2)]

➠(3b - 5b²)/5 = -2/5

➠5b² -3b -2 = 0

➠5b² -5b +2b -2 = 0

➠5b (b-1) +2 (b-1) = 0

➠(b-1) (5b+2) = 0

➠b-1 = 0

➠$\boxed{\sf{ b=1 }}$

➠5b + 2 = 0

➠5b = -2

➠$\boxed{\sf{ b = -2/5 }}$

(1)➜ a + b = 3/5 [from (1)]

➠a - 2/5 = 3/5

➠a = 3/5 + 2/5

➠a = 5/5

➠$\boxed{\sf{ a = 1 }}$

➠a³ + b³

➠(1)³ + (-2/5)³

➠1 - (8/125)

➠125-8 /125

➠$\boxed{\sf{117 / 125 }}$