If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.

If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³.

Sum

125x³ − 64y³ = (5x)³ − (4y)³

= (5x − 4y)³ + 3(5x) (4y) (5x − 4y)

= (5x − 4y)³ + 60xy (5x − 4y)

= (7)³+ 60 (8) (7)

= 343 + 3360

= 3703

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Application of Formulae

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Chapter 12: Identities - Exercise 12 (D) [Page 155]

Chapter 12 Identities
Exercise 12 (D) | Q 15 | Page 155

If a – b = 6 and ab = 16, find a² + b²

If a + b + c = 10 and a² + b² + c² = 38, find : ab + bc + ca

Find : a + b + c, if a² + b² + c² = 83 and ab + bc + ca = 71.

If `2"x"-1/(2"x")=4`, find : `4"x"^2+1/(4"x"^2)`

If `2"x"-1/(2"x")=4`, find: `8"x"^3-1/(8"x"^3)`

If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`

The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.

If a² + b² = 41 and ab = 4, find : a – b

If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³.

The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.