SOLUTION: the difference of squares of two numbers is 88.If the larger number is 5 less than twicw the smaller one ,then find the two nubers?

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Question 613980: the difference of squares of two numbers is 88.If the larger number is 5 less than twicw the smaller one ,then find the two nubers?
Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
Let the smaller number be x
Now the larger number = 5 less thann 2 times the smaller number
= 2x -5
Difference of the sqaures of the 2 numbers is 88
%282x-5%29%5E2+-+x%5E2=88
=>4x%5E2+-20x+%2B+25+-x%5E2=88
=>3x%5E2+-+20x+-+63=0 Grouping the common terms together
=>x=+%28-%28-20%29%2B-+sqrt%28400+-+4%2A3%2A+-63%29%29%2F%282%2A3%29
=>x=+%2820%2B-+sqrt%28400%2B756%29%29%2F6
=>x=%2820%2B-sqrt%281256%29%29%2F6
=>x=%2820%2B%2834%29%29%2F6+and x=%2820-%2834%29%29%2F6++
=>x=54%2F6+and x=+-14%2F6
=>x=9+and+x=-7%2F3
Therefore the smaller number is 9 and the bigger number is 2*9-5= 13
Ignoring the negative -7/3 as 2 times this number - 5 that is (-14/3 -5 =-29/5),gives a smaller number and not a larger number as in the problem statement