if a-b=3 and ab equals to 4, find a^3-b^3
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Answered by
2
Given a - b = 3 and ab= 4.
We know that a^3-b^3 = (a-b)^3 + 3ab(a-b)
= (3)^3 + 3*4(3)
= 27 + 36
= 63.
Hope this helps!
We know that a^3-b^3 = (a-b)^3 + 3ab(a-b)
= (3)^3 + 3*4(3)
= 27 + 36
= 63.
Hope this helps!
JunaidMirza:
Check your calculations
The answer will be 63.My Mistake. I have written (3)^3 as 9.But I cannot correct it now
Answered by
2
ab = 4
b = 4/a
a - b = 3
a - 4/a = 3
a² - 4 = 3a
a² - 3a - 4 = 0
a² - 4a + a - 4 = 0
a(a - 4) + (a - 4) = 0
(a + 1) · (a - 4) = 0
a = -1 or a = 4
If a = -1 then b = -4 ……[∵ ab = 4]
So,
a³ - b³ = (-1)³ - (-4)³ = -1 + 64 = 63
If a = 4 then b = 1 ……[∵ ab = 4]
So,
a³ - b³ = (4)³ - (1)³ = 64 - 1 = 63
∴ a³ - b³ = 63
b = 4/a
a - b = 3
a - 4/a = 3
a² - 4 = 3a
a² - 3a - 4 = 0
a² - 4a + a - 4 = 0
a(a - 4) + (a - 4) = 0
(a + 1) · (a - 4) = 0
a = -1 or a = 4
If a = -1 then b = -4 ……[∵ ab = 4]
So,
a³ - b³ = (-1)³ - (-4)³ = -1 + 64 = 63
If a = 4 then b = 1 ……[∵ ab = 4]
So,
a³ - b³ = (4)³ - (1)³ = 64 - 1 = 63
∴ a³ - b³ = 63
Thank You JunaidMirza
You’re welcome
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