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प्रश्न
If 2x – 3y – 4z = 0, then find 8x3 – 27y3 – 64z3
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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
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संबंधित प्रश्न
Find the following product: (x + 7) (x − 5)
Multiply the following:
(3x2 + 4x – 8), (2x2 – 4x + 3)
Multiply the following:
(2x – 2y – 3), (x + y + 5)
Simplify:
(a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab)
Expand the following, using suitable identities.
(x2y – xy2)2
Expand the following, using suitable identities.
(x + 3)(x + 7)
Carry out the following division:
–121p3q3r3 ÷ (–11xy2z3)
Perform the following division:
(3pqr – 6p2q2r2) ÷ 3pq
Perform the following division:
(ax3 – bx2 + cx) ÷ (– dx)
Match the expressions of column I with that of column II:
| Column I | Column II |
| (1) (21x + 13y)2 | (a) 441x2 – 169y2 |
| (2) (21x – 13y)2 | (b) 441x2 + 169y2 + 546xy |
| (3) (21x – 13y)(21x + 13y) | (c) 441x2 + 169y2 – 546xy |
| (d) 441x2 – 169y2 + 546xy |
