Question

the product of two consecutive even numbers is 1088 which is larger number

Answer 1

Hi there !

Let the number be 2x and 2x+2.
Then,
2x × (2x+2)=1088
x(2x+2)=544
2x^2 +2x-544=0
x^2 +x -272=0
x^2 +17x-16x -272=0
x(x+17) -16(x+17)=0
(x+17)(x-16)=0
Therefore, x+17=0 or x-16=0
Then,x=-17 or x=16.

Consecutive even number are either 2x=32 and 2x+2=34 or 2x=-34 or 2x+2=-32.

Hence the larger number is 34.

Answer 2

Let even numbers be 2x,(2x+2)
given (2x)(2x+2)=1088
=>4(x^2)+4x=1088
=>4[(x^2+x]=1088
=>x^2+x=272
=>x(x+1)=272
=>x(x+1)=16(17)
hence x=16
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