Math, asked by pranshugupta468, 4 months ago

If x + y = 9 and xy = 14, find x2 - y2.​

Answers

Answered by astha1917
1

Step-by-step explanation:

x + y = 9 )-------(1)

xy = 14 )----------(2)

from equation (2)

  • x =  \frac{14}{y}

putting value of x in equation (1)

 \frac{14}{y}  + y = 9

 \frac{14  +  y {}^{2} }{y}  = 9

14 + y {}^{2}  = 9y

y {}^{2}  - 9y + 14 = 0

according to mid term splitting method,

y {}^{2}  - 7y - 2y  + 14 = 0

(y - 2)(y - 7) = 0

we got value is y as ,

  • y = 2 , 7

putting value of y = 2in equation of X,

  • x  =  \frac{14}{2}
  • x = 7

keeping x = 7 and y = 2 in equation given in the question,

x {}^{2}  - y {}^{2}  = 7 {}^{2}  - 2 {}^{2}

 x {}^{2}  - y {}^{2}  = 49 - 4

x {}^{2}  - y {}^{2}  = 45

answer from values

x = 2,7

y = 7,2

can be find accordingly.

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