Find the value of (4+√15)³ - (4-√15)³ with the help of identity
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Answer:
128√15
Step-by-step explanation:
use the identity a³ - b³ = (a-b) (a² + ab + b²)
=> a = 4+√15 and b = 4 - √15
ab = (4+√15)(4 - √15) = 16 - 15 = 1
a - b = 4 + √15 - 4 + √15 = 2√15.
//find out a² + b², by squaring the above equation on both sides.
(a-b)² = (2√15)²
a²+ b² = 60 + 2ab = 60 + 2 = 62
//Now substitute the values in a³ - b³ = (a-b) (a² + ab + b²)
=> 2√15(62+2)
=> 128√15.
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