Question

If x + 2y = 8 and xy = 6, find the value of x3

+ 8y3

.​

Answer 1

Answer:

Answer: 224

Algebra:

Method 1:

We have the identity a³ + b³ = (a+b)³ - 3ab (a+b) …………………………………….(1)

Rewriting, x³ + 8y³ = (x)³ + (2y)³

which is of the form a³ + b³ where a=x and b=2y.

Substituting the above values of a and b in (1),

x³ + 8y³ = (x+2y)³ - 3x.2y (x + 2y) = (x+2y)³ - 6xy (x + 2y)……………………………(2)

But we are given that x+2y = 8 and xy = 6. Substitute these values in (2) and obtain,

x³ + 8y³ = (8)³ - 6.6 (8) = 512 - 288

= 224 (Answer)

Method 2:

We have the identity a³ + b³ = (a+b) (a² - ab + b²) …………………………………….(α)

Rewriting, x³ + 8y³ = (x)³ + (2y)³

which is of the form a³ + b³ where a=x and b=2y.

Substituting the above values of a and b in (α),

x³ + 8y³ = (x + 2y) (x² - 2xy + 4y²) = (x + 2y) [x² + 2.x.2y + (2y)² - 6 xy]

= (x + 2y) [(x + 2y)² - 6xy]……………………………………………………………………….(β)

Given, x+2y = 8 and xy = 6. Substituting in (β),

x³ + 8y³ = 8 (8² - 6.6) = 8(64 - 36) = 8 x 28

= 224 (Answer)

Step-by-step explanation:

Answer 2

Answer:

42

Step-by-step explanation:

because if x=6 and y=1 then 6+2×1=8 and 6×1=6 , therefore 6×3+8×1×3= 18+24=42

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