Question

if x = 1 / 4 - square rot of 15 and y = 1/4+square root of 15 what is the value of x cube + y cube

Answer 1

x³ + y³ = 488

Step-by-step explanation:

Given,

x = 1/(4 - √15)

= (4 + √15)/{(4 - √15)(4 + √15)}

= (4 + √15)/(16 - 15)

= 4 + √15

y = 1/(4 + √15)

= (4 - √15)/{(4 + √15)(4 - √15)}

= (4 - √15)/(16 - 15)

= 4 - √15

Then x³ + y³

= (4 + √15)³ + (4 - √15)³

= (4 + √15 + 4 - √15) {(4 + √15)² - (4 + √15) (4 - √15) + (4 - √15)²}

= 8 {(16 + 8√15 + 15) - (16 - 15) + (16 - 8√15 + 15)}

= 8 (31 + 8√15 - 1 + 31 - 8√15)

= 8 * 61

= 488

Rule:

• a³ + b³ = (a + b) (a² - ab + b²)

• a³ - b³ = (a - b) (a² + ab + b²)