if x + 2y = 8 and xy = 6, find the value of x³ + 8y³ = ?
→ x + 2y = 8
cubing both sides, we get,
→ (x + 2y)³ = 8³
using (a + b)³ = a³ + b³ + 3ab(a + b) in LHS, we get,
→ x³ + (2y)³ + 3 * x * 2y * (x + 2y) = 512
→ x³ + 8y³ + 6xy * (x + 2y) = 512
putting xy = 6 Now,
→ x³ + 8y³ + 6 * 6 * (x + 2y) = 512
putting (x + 2y) = 8 Now,
→ x³ + 8y³ + 36 * 8 = 512
→ x³ + 8y³ + 288 = 512
→ x³ + 8y³ = 512 - 288
→ x³ + 8y³ = 224 (Ans.)
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Qᴜᴇsᴛɪᴏɴ :-
if x + 2y = 8 and xy = 6, find the value of x³ + 8y³ = ?
Sᴏʟᴜᴛɪᴏɴ :-
→ x + 2y = 8
cubing both sides, we get,
→ (x + 2y)³ = 8³
using (a + b)³ = a³ + b³ + 3ab(a + b) in LHS, we get,
→ x³ + (2y)³ + 3 * x * 2y * (x + 2y) = 512
→ x³ + 8y³ + 6xy * (x + 2y) = 512
putting xy = 6 Now,
→ x³ + 8y³ + 6 * 6 * (x + 2y) = 512
putting (x + 2y) = 8 Now,
→ x³ + 8y³ + 36 * 8 = 512
→ x³ + 8y³ + 288 = 512
→ x³ + 8y³ = 512 - 288
→ x³ + 8y³ = 224 (Ans.)