Find the value of a^3-27b^3 if a-3b =-6, ab = -10
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Answered by
3
[tex] {a}^{3} - 27 {b}^{3} = {a}^{3} - (3b {)}^{3}
using identity a^3-b^3 = (a-b)(a^2+ab+b^2)
= a^3-(3b)^3 = (a-3b)[a^2+a×3b+(3b)^2]
by putting the values
(-6)(a^2+3×-10+9b^2)
(-6)(a^2-30+9b^2). -(1)
(a-3b)^2= a^2-2×a×3b+(3b)^2 = (-6)^2
a^2 -6×10+9b^2 = 36
a^2-60+9b^2 = 36
a^2+9b^2 = 36+60 = 96
a^2+9b^2 = 96
putting this value in equation 1
(-6)(a^2-30+9b^2)
(-6)(96-30)
(-6)(66)
-396
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using identity a^3-b^3 = (a-b)(a^2+ab+b^2)
= a^3-(3b)^3 = (a-3b)[a^2+a×3b+(3b)^2]
by putting the values
(-6)(a^2+3×-10+9b^2)
(-6)(a^2-30+9b^2). -(1)
(a-3b)^2= a^2-2×a×3b+(3b)^2 = (-6)^2
a^2 -6×10+9b^2 = 36
a^2-60+9b^2 = 36
a^2+9b^2 = 36+60 = 96
a^2+9b^2 = 96
putting this value in equation 1
(-6)(a^2-30+9b^2)
(-6)(96-30)
(-6)(66)
-396
hope this helps you plz mark as brainliest answer plzzzzz
Raj2291:
here we have to find the value of A and B and that value is substitutting in given equation to find the value of that equation.
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Answered by
5
Answer:
a3 - 27b3=?
a-3b=-6
ab=-10
using (a-b)3=a3-b3-3ab(a-b)
(a-3b)=(a)3-(3b)3-3ab(a-3b)
(-6)3 =(a)3 - (3b)3 - 3(-10)(-6)
a3-27b3 = -216+180
ANSWER =a3-27b3 = -36
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