यदि `x + y + z = 1, xy + yz + zx = -1` व xyz = -1, तब `x^(3)+y^(3)+z^(3)` का मान ज्ञात कीजिए ।

Explanation

हम जानते है की ` x^(3) + y^(3) + z^(3) - 3 xyz = ( x + y + z) (x^(2) + y^(2) + z^(2) - xy - yz - zx)`
` rArr x^(3) + y^(3) + z^(3) - 3 xyz`
` = ( x+ y + z) ( x^(2) + y^(2) + z^(2) + 2xy+ 2yz + 2zx - 3xy - 3yz - 3zx)`
` [ 2xy + 2yz + 2zx " को जोड़ने तथा घटाने पर "]`
` rArr x^(3) + y^(3) + z^(3) - 3 xyz = ( x+ y+ z) {(x+y+z)^(2)- 3 (xy + yz + zx)}`
`rArr x^(3) + y^(3) + z^(3) - 3 xx 1 = 1 xx {(1)^(2) - 3 xx 1 }" " [ x+y+z =1" तथा " xy+ yz+ zx = - 1 " xyz = -1 रखने पर "] `
` rArr x^(3) + y^(3) + z^(3) + 3 = 4 `
` rArr x^(3) + y^(3) + z^(3) = 4-3 `
` rArr x^(3) + y^(3) + z^(3) = 1`