74th Problem 2016

Algebra Level 2

The product of 2 consecutive integers is 30. Find the largest negative integer of the two integers.

Check out the set: 2016 Problems


The answer is -5.

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Angela Fajardo
Mar 23, 2016

Let:

x = 1 s t n u m b e r x + 1 = 2 n d n u m b e r x=1st\quad number\\ x+1=2nd\quad number

x ( x + 1 ) = 30 x 2 + x = 30 x 2 + x − 30 = 0 ( x − 5 ) ( x + 6 ) = 0 x = 5 ∣ x = − 6 x + 1 = 6 ∣ x + 1 = − 5 x\left( x+1 \right) =30\\ { x }^{ 2 }+x=30\\ { x }^{ 2 }+x-30=0\\ \left( x-5 \right) \left( x+6 \right) =0\\ x=5\quad |\quad x=-6\\ x+1=6\quad |\quad x+1=-5

Largest Negative Integer: -5

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Why negative? to make it confusing?

Austin Li - 12 months ago

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