Question

यदि x - y = 4 तथा xy = 21 तो x3 - y3 का मान ज्ञात करो​

Answer 1

Answer:

x³-y³ = 316

Step-by-step explanation:

x - y = 4

Cubing both side,

(x - y)³ = 4³

x³-y³-3xy(x-y) = 64 [Using (x-y)³ identity]

x³-y³ -3(21)(4) = 64 [xy = 21 , x-y = 4]

x³-y³-252 = 64

x³-y³ = 64 + 252

x³-y³ = 316

Answer 2

Answer:

$x - y = 4 \\ x = 4 + y \\ \\ xy = 21 \\ (4 + y)y = 21 \\ 4y + {y}^{2} = 21 \\ {y}^{2} + 4y - 21 = 0 \\ {y}^{2} + 7y - 3y - 21 = 0 \\ y(y + 7) - 3(y + 7) = 0 \\ (y + 7)(y - 3) = 0 \\ y + 7 = 0 \: \: \: or \: \: \: y - 3 = 0 \\ y = \underline{ \underline{ - 7}} \: \: \: or \: \: \: y = \underline{ \underline{3}} \\ \\ x - y = 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - y = 4 \\ x - ( - 7) = 4 \: \: \: or \: \: \: x - 3 = 4 \ \\ x + 7 = 4 \: \: \: \: or \: \: \: \:x - 3 = 4\\ x = 4 - 7 \: \: \: \: or \: \: \: \: x = 4 + 3\\ x = \underline{ \underline{ - 3}} \: \: \: or \: \: \: x = \underline{ \underline{7}}$