Math, asked by anjali6557, 1 year ago

X cube + y cube = 28 and X square and y square = 10 then find the value of X and y​

Answers

Answered by abhi178
3

it is given that,

x³ + y³ = 28 and x² + y² = 10

now, x³ + y³ = 28

or, (x + y)³ - 3xy(x + y) = 28 ....(1)

[ as we know, a³ + b³ = (a + b)³ - 3ab(a + b) ]

again, x² + y² = 10

or, (x + y)² - 2xy = 10 ......(2)

[ as we know, a² + b² = (a + b)² - 2ab]

Let (x + y) = p

from equations (1) and (2),

p³ - 3p(p² - 10)/2 = 28

or, 2p³ - 3p³ + 30p = 56

or, p³ - 30p + 56 = 0

or, p³ - 4p² + 4p² - 16p - 14p + 56 = 0

or, p²(p - 4) + 4p(p - 4) - 14(p - 4) = 0

or, (p² + 4p - 14)(p - 4) = 0

or, p = 4, p² + 4p - 14 = 0

for getting integers value , take p = 4

putting p = (x + y) = 4 in equation (2),

(4)² - 2xy = 10

or, xy = 3

from solving we get, x = 3 and y = 1 or , x = 1 and y = 3 .

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