Latest Self Aptitude Question SOLUTION: Sum of 2 nos.is 8 and their product is 13.11. Find the nos.

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Sum of 2 nos.is 8 and their product is 13.11. Find the nos.

RAMADURAI NATESAN (5 years ago)

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Devendra Marghade  (5 years ago)

2.3, 5.7

Let the numbers be x and (8-x), then x(8-x)=13.11
=> x² -8x + 13.11 = 0
Equation is of the form ax² + bx + c = 0
Root are given by [-b ± √(b² - 4ac)] / 2a = [8 ± √(64-52.44)]/2 = (8 ± √11.56 )/2
Hence roots are (8+3.4)/2=5.7 and (8-3.4)/2=2.3

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RAMADURAI NATESAN  (5 years ago)

As. sum is 8, average/midpoint is 4, from which the 2 nos will be equidistant by an unknown factor + or -d .Hence let the 2 nos.be 4+d and 4-d .Sum is 4+d+4-d = 8.Product is (4+d) *(4-d) =16-dsq.=13.11(Given).
dsq.=16-13.11 =2.89. d=root of 2.89 = 1.7. Hence nos are 4+1.7 and 4-1.7 i.e, 5.7 and 2.3. Here I have not used quadratic equation ,its roots etc.Pl.put this solution in your site for the benefits of your students.In general ,by the same method it can easily be proved that if sum of 2 nos is S and product is P then the nos are :(S/2) +or-sq.root of((Ssq./4)-P))

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