If x-y-5 and x y-6- then find x3-y3x-y -4 marks-

As, (x−y)^2 = (x+y)^2 − 4xy (Identity) (x y)^2 = 25 24 or , x−y=+1,−1now equation 1 = gt; x+y=5x+y=5and equation 2 = gt; x−y=+1,−1By solving the two equat ...

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Byju's Answer

Standard IX

Mathematics

(x±a)(x±b) = x²±(a+b)x+ab.

If x+y=5 and ...

Question

If x+y=5 and xy=6, then find x³-y³(x>y) [4marks]

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Solution

As, (x−y)^2 = (x+y)^2 − 4xy
(Identity) (x-y)^2 = 25 - 24 or
, x−y=+1,−1now equation 1 => x+y=5x+y=5and equation 2 => x−y=+1,−1By solving the two equation we get,x=3,y=2or,x=2,y=3
So, Case 1: x=3,y=2:
x^3-y^3 = 19
Case 2: x=2,y=3:
x^3-y^3 = -19

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If x+y=5 and xy=6, then find x3-y3 (x>y) [4marks]

As, (x−y)^2 = (x+y)^2 − 4xy (Identity) (x-y)^2 = 25 - 24 or , x−y=+1,−1now equation 1 => x+y=5x+y=5and equation 2 => x−y=+1,−1By solving the two equation we get,x=3,y=2or,x=2,y=3 So, Case 1: x=3,y=2: x^3-y^3 = 19 Case 2: x=2,y=3: x^3-y^3 = -19

If x+y=5 and xy=6, then find x³-y³(x>y) [4marks]

As, (x−y)^2 = (x+y)^2 − 4xy
(Identity) (x-y)^2 = 25 - 24 or
, x−y=+1,−1now equation 1 => x+y=5x+y=5and equation 2 => x−y=+1,−1By solving the two equation we get,x=3,y=2or,x=2,y=3
So, Case 1: x=3,y=2:
x^3-y^3 = 19
Case 2: x=2,y=3:
x^3-y^3 = -19