English, asked by ananyaghosh666, 4 months ago

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Answers

Answered by Anonymous
24

Explanation:

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☘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}}

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 }}

b=1

➠5b + 2 = 0

➠5b = -2

➠\boxed{\sf{ b = -2/5 }}

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 }}

a=1

➠a³ + b³

➠(1)³ + (-2/5)³

➠1 - (8/125)

➠125-8 /125

➠\boxed{\sf{117 / 125 }}

117/125

Answered by Tsubhiksha
0

Explanation:

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