Question
If 64x3 - 343y3 = (4x - Ay) X (Bx2 + 49y2 + Cxy), then find the value of 3 X (2A + 6
- B - 2C.
Solution
64x3 - 343y3 = (4x - Ay) X (Bx2 + 49y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 64x3 - 343y3 = (4x)3 - (7y)3 = (4x - 7y) X (16x2 + 49y2 + 4x X 7y) = (4x - 7y) X (16x2 + 49y2 + 28xy) So, (4x - Ay) X (Bx2 + 49y2 + Cxy) = (4x - 7y) X (16x2 + 49y2 + 28xy) On comparing coefficients of LHS and RHS, we get, A = 7, B = 16, and C = 28 So, 3 X (2A + 6B) - 2C = 3 X {2 X 7 + 6 X 16} - 2 X 28 = 3 X (14 + 96) - 56 = 3 X 110 - 56 = 330 - 56 = 274
More Algebra Questions
- If x² - 2x + 1 = 0, then find the value of (x⁴ + x⁻⁴)(x + x⁻¹).
- If x + 1/x = 3, then [x3 + (1/x3)] = ?
- If x = 10 + 2√21, then the value of √x - (1/√x)?
- If (2a + b)/(3b - 2b) = 13/2 then 'b' is what percent of 'a'?
- `sqrt(sqrt(10+sqrt(10+sqrt(10)) ... prop)` = ?
- If (x + y) = 35, then find the value of (x - 10)6 + (y - 25)6.
- If a + `1/b` = 1 and b + `1/c` =1 , then the value of c + `1/a` is
- Find ‘x’ if (x³+3x)/(3x²+1) = 189/61
- If x + y = 2 and 1/x + 1/y = 18/15, then find the value of (x3 + y3)?
- If 112 ÷28 x 22 –12 x 6 ÷ 3 +12 = z, then find the value of z.
