find the two numbers whose product is 150 difference is 5 and sum is 25
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Answer:
xy=150 (Eq 1)
x-y=5 (Eq 2)
x+y=25. ( Eq 3)
Let us see what result we get by solving 3 pairs of equations one by one
Using Eq 1 and Eq 2
y=150/x, x- 150/x=5, x^2–5x-150=0, x=[5+-sqrt(25+600)]/2= [5+-25]/2= 15 or -10, y= x-5= 10 or -15
Thus the values of (x,y) are (15,10) or (-10,-15), Also satisfies xy=150
Using Eq 2 and Eq 3
2x=30, x=15, y=25-x=10
Thus the values of (x,y) are (15,10) , Also satisfies xy=150
Using Eq 2 and Eq 3
x+150/x=25, x^2–25x+150=0, x= [25+-sqrt(625–600)]/2= (25+-5)/2= 15 or 10, y= 25-x= 10 or 15
Thus the values of (x,y) are (15,10) or (10,15), also satisfies xy=150
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