x2 + y2 =29 , y - x = 3 find the value of x & y

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(-5, 2) and (-2, 5)

(5, -2) and (2, -5)

(-5, -2) and (2, 5)

(-5, -3) and (3, 5)

answer is C.

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Detailed Solution

x2 + y2 =29 …(i)
y – x = 3 …(ii)
from (ii)
y= 3 + x …(iii)
put value of y from (iii) into (i)
x2 + (3 + x )2 =29 [(a + b)2 = a2 + b2 +2ab ]
x2 + 9 + x2 +6x = 29
2x2 + 6x -20 = 0 [taking 2 common from L.H.S and sending it to R.H.S]
x2 + 3x – 10 = 0
x2 + 5x – 2x – 10 = 0
x(x + 5) -2(x+5) = 0
(x+ 5)( x - 2)=0 …(iv)
From (iv) we know x = -5 or 2
Putting these value of x in (iii)
Put x = -5
y = 3 – 5
y = -2
put x = 2
y = 3 + 2
y = 5
therefore value of x and y will be (-5, -2) and (2, 5)

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