Question

pls help me
$x - y = 4 \ \\ x {}^{3} - y {}^{3} = 316 \\ xy = {?} \\ x {}^{2} + y {}^{2} = {?}$

Answer 1

${x }^{ 3 } - { y}^{ 3 } = 316$
x - y = 4

On cubing both sides, we get

x^3 - y^3 - 3xy ( x - y) = 64

=> 316 - 3xy( 4) = 64

=> 316 - 64 = 12xy

=> 12xy = 252

=> xy = 21

Now,
${x }^{ 2} + { y }^{2 } = { ( x - y) }^{ 2 } + 2xy$

= { 4 }^{ 2 } + 2 × 21

= 16 + 42

= 58

Answer 2

Answer:

⭐ SOLUTION ⭐

x³-y³ = 316

x - y = 4

➡ On cubing both side we get,

x³ - y³ - 3xy(x-y) = 64

=> 316 - 3xy (4) = 64

=> 316 - 64 = 12xy

=> 12xy = 252

➡ Now,

x² + y² = (x-y)² + 2xy

= (4)² + 2 × 21

= 16 + 42

= 52

Step-by-step explanation:

HOPE IT HELP YOU