Question

factorize 216x^6-793x^3+216=0​

Answer 1

Answer:

(8x³-27) (27x³-8) = 0

Step-by-step explanation:

216x^6-793x^3+216=0​   ..... (1)

By multiplying the coefficient of the 1st term by the constant, we get

216 × 216 = 46656

Finding the two factors of 46656, such that its sum is equal to 793

Thus

729 x 64 = 46656   &    729 + 64 = 793

Thus the two factors are 729 and 64,

Re-writing the eq(1), by spliting the middle term in 2 factors as above we get,

∵216x^6 - 793x^3  +216=0​

∴ 216x^6 - 729x^3 - 64x^3 + 216=0​

Taking common factors outside the bracket

∴ 27x³(8x³-27) - 8(8x³-27) = 0

∴ (8x³-27) (27x³-8) = 0

Answer 2

Answer:

x = 2/3  or x = 3/2

Step-by-step explanation:

Factorize 216x^6-793x^3+216=0​

216x⁶ - 793x³  + 216 = 0

=> 216x⁶ - 729x³ - 64x³ + 216 = 0

=> 27x³(8x³ - 27) - 8(8x³ - 27) = 0

=> (27x³ -8)(8x³ - 27) = 0

=> x³ = 8/27   or  x³ = 27/8

=> x³ = 2³/3³   or  x³ = 3³/2³

=> x³ = (2/3)³   or  x³ = (3/2)³

=> x = 2/3  or x = 3/2