The product of two consecutive natural number is 31 less than the sum of their squares. Find the number
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2
Answer:
Let two consecutive natural numbers be xx and x+1x+1.
Sum of these numbers
=x+x+1=x+x+1
=2x+1=2x+1
Difference of their squares (from largest)
=(x+1)2−x2=(x+1)2−x2
=x2+2x+1−x2=x2+2x+1−x2
=2x+1=2x+1
∴∴ Both are equal.
So the answer is also 31.
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Answered by
0
Answer:
let first number =x,second number=x+1
Step-by-step explanation:
the product of two consecutive natural numbers is 31 less than their sum of squares
so
x(x+1)= x square+ ( x+1) whole square-31
x square+ x= 2x square+2x+1-31
2x square- x square+ 2x-x+1-31
x square+x-30=0
x square+6x-5x-30=0
x(x+6)-5(x+6)=0
(x-5),(x+6)=0,x=5;x+1=6
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