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25.01.2020 •
Mathematics
Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
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Ответ:
The three consecutive natural numbers are 9,10,11
Step-by-step explanation:
Step 1 : -
Let x be the number
Given three consecutive natural numbers are x, x+1,x+2
Given data are three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
that is [tex](x+1)^2 = (x+2)^2 - x^2 +60{\tex]
step 2:-
on simplification on both sides are , we get
by using [tex](a+b)^2 = a^2+2 a b+b^2[\tex]
[tex]x^2+2 x+1 = x^2+4 x+4-x^2+60[\tex]
cancelling x^2 terms and simplify
[tex] x^2 -2 x-63=0[\tex]
now finding factors of [tex] 63 = 9 X 7[\tex]
[tex] x^2 - 9 x+7 x -63=0 [\tex]
[tex] x(x-9)+7(x-90 =0 [\tex]
[tex]( x+7)(x-9) =0 [\tex]
here x= -7 is not an natural number
so we have to take x=9
therefore the three consecutive natural numbers are
x,x+1,x+2
The three consecutive natural numbers are 9 , 10, 11
Ответ:
Organizes Data
Step-by-step explanation:
A table can help you organize information, and it can show patterns you can make tables with time, line plots, graphs