Question

find the value of 64x^3 + 125z^3 , if 4x+5z=19 and xz=5



pls pls answer with clear steps understand its an emergency dont post senseless answer

Answer 1

Given, 4x + 5z = 19 and xz = 5

4x + 5z = 19

Cubing on both sides, we get

(4x + 5z)3 = (19)3

⇒ (4x)3 + (5z)3 + 3 × 4x × 5z (4x + 5z) = 6859

⇒ 64x3 + 125z3 + 60xz (4x + 5z) = 6859

⇒ 64x3 + 125z3 + 60 × 5 × 19 = 6859                    ( 4x + 5z = 19 & xz = 5)

⇒ 64x3 + 125z3 + 5700 = 6859

⇒ 64x3 + 125z3 = 6859 – 5700 = 1159

Thus, the value of 64x3 + 125z3 is 1159.


hope this helps you..!!

Answer 2

$4x + 5z = 19 \\ xz = 5 \\ 64 {x}^{3} + 125 {z}^{3} = ( {4x})^{3} + ( {5z)}^{3} \\ apply \: the \: identity \\ = (4x + 5z)(16 {x}^{2} - 20xz + 25 {z}^{2} ) \\ = 19(16 {x}^{2} + 40xz + 25 {z}^{2} - 60xz) \\ = 19(( {4x + 5z)}^{2} - 60xz) \\ = 19( {19}^{2} - 60 \times 5) \\ = 19(361 - 300) \\ = 19 \times 61 \\ = 1159$