if a + b is equals to 12 and a b is equal to 27 find the value of a cube plus b cube
Answers
Answer:
a³ + b³ = 756
Step-by-step explanation:
a + b = 12 ------(1)
ab = 27 ------(2)
from eq. 1
a + b = 12
a = 12 - b
put a in eq. 2
ab = 27
(12 - b)b = 27
12b - b² = 27
b² - 12b + 27 = 0
b² - 9b - 3b + 27 = 0
b(b - 9)*-3(b - 9) = 0
(b - 9)(b - 3) = 0
b = 9 or b = 3
put b in eq. 1
(if, b = 3) a + b = 12
a + 3 = 12
a = 12 - 3
a = 9
(if, b = 9) a + 9 = 12
a = 12 - 9
a = 3
now, a³ + b³ (if a=3 and b=9)
= (3)³ + (9)³
= 27 + 729
= 756
or, if a = 9 and b = 3
then, a³ + b³
= (9)³ + (3)³
= 729 + 27
= 756
so , a³ + b³ = 756
Step-by-step explanation:
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