Advertisements
Advertisements
प्रश्न
If 2x – 3y – 4z = 0, then find 8x3 – 27y3 – 64z3
Advertisements
उत्तर
We know x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
x3 + y3 + z3 = (x + y + z) (x2 + y2 + z2 – xy – yz – zx) + 3xyz
8x3 – 27y3 – 64z3 = (2x)3 + (– 3y)3 + (– 4z)3
= (2x – 3y – 4z) [(2x)2 + (– 3y)2 + (– 4z)2 – (2x)(– 3y) – (– 3y)(– 4z) – (– 4z)(2x)] + 3(2x)(– 3y)(– 4z)
= 0 (4x2 + 9y2 + 16z2 + 6xy – 12yz + 8xz) + 72xyz
= 72xyz
8x3 – 27y3 – 64z3 = 72xyz
APPEARS IN
संबंधित प्रश्न
Show that `(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2`
If 2x + 3y = 14 and 2x − 3y = 2, find the value of xy.
[Hint: Use (2x + 3y)2 − (2x − 3y)2 = 24xy]
Find the following product: (x + 4) (x + 7)
Find the following product: (y2 − 4) (y2 − 3)
Evaluate the following: 109 × 107
Evaluate the following: 53 × 55
Using algebraic identity, find the coefficients of x2, x and constant term without actual expansion
(x + 5)(x + 6)(x + 7)
Expand the following, using suitable identities.
(x2y – xy2)2
Perform the following division:
(x3y3 + x2y3 – xy4 + xy) ÷ xy
Perform the following division:
(– qrxy + pryz – rxyz) ÷ (– xyz)
