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(a-b)=3 and ab=5 then a³-b³=
Given the equations (a-b) = 3 and ab = 5, we can find the value of a³-b³.
Equation 1: (a-b) = 3
From this equation, we can express b in terms of a:
b = a - 3 ... (1)
Equation 2: ab = 5
Substituting equation (1) into equation (2), we get:
a(a - 3) = 5
Expanding the equation, we get:
a² - 3a - 5 = 0
Factoring the equation, we get:
(a - 5)(a + 1) = 0
This gives us two possible values for a:
a = 5 or a = -1
Finding the value of a³-b³
Now, we can find the value of a³-b³ using the values of a and b.
Case 1: a = 5 and b = 2 (from equation 1) a³ = 5³ = 125 b³ = 2³ = 8 a³ - b³ = 125 - 8 = 117
Case 2: a = -1 and b = -4 (from equation 1) a³ = (-1)³ = -1 b³ = (-4)³ = -64 a³ - b³ = -1 - (-64) = 63
Therefore, the value of a³-b³ is 117 or 63, depending on the values of a and b.
