Question

if 3m-2n=5 and mn=6 then find the values of 27m3-8n3​

Answer 1

Given: 3m - 2n = 5 and mn = 6

To find: The value of 27m³ - 8n³

Solution:

• Now we have given:

                 3m - 2n = 5 and mn = 6

                 n = 6/m

• Putting n in first equation, we get:

                 3m - 2(6/m) = 5

                  3m - 12/m = 5

                  3m² - 12 = 5m

                  3m² - 5m - 12 = 0

• Now by middle term splitting, we get:

                  3m² - 9m + 4m - 12 = 0

                  3m(m-3) + 4(m-3) = 0

                  m = 3

• Putting m in  n = 6/m , we get:

                 n = 2

• Now putting value of m and n in 27m³-n³, we get:

                 27m³-n³ = 27(3)³-(2)³

              = 27(27) - 8

              = 729 - 8

              = 721

Answer:

              So the value of 27m³-n³ is 721.

Answer 2

Answer:

Given

3m - 2n =5 & mn = 6

(3m -2n)^3 = 5^3

we know that ( a-b)^3 = a^3 -b^3 -3ab (a-b)

= (3m)^3 - (2n)^3 - 3.3m.2n ( 3m-2n) = 125

= 27m^3 - 8n^3 - 18mn (5) = 125

27m^3 - 8n^3 - 18 (6) (5) = 125

27m^3 - 8n^3 - 540 = 125

27m^3 - 8n^3 = 125 + 540

27m^3 - 8n^3 = 665

therefore values of 27m^3 -8n^3 = 665