Difference of 2 squares

Algebra Level 1

The difference of the squares of 2 consecutive integers is 29. What is the product of these 2 integers?

210 110 240 29

2 solutions

Agastya Chandrakant
Jan 31, 2015

$(a+1)^{ 2 }-{ a }^{ 2 }=29$
or, $(a+1+a)\times (a+1-a)=29$
or, $(2a+1)=29$
therefore $a=14$ $14\times 15=210$

You missed out another solution, which correspond to $a = -15$ .

The issue is that the first equation should be $| ( a+1)^2 - a^2 | = 29$ . At the end, we have $(-15) \times (-14) = 210$ , so it turns out to be the same.

If we asked for the sum, the the sum could have been -29.

Chung Kevin - 6 years, 4 months ago

While preparing for entrance exams: we are asked to develop a mentality that just find the answer as our first target is JEE mains having only one correct answer. so 210 is what i need to compute!

Agastya Chandrakant - 6 years, 4 months ago

Indeed, as you stated, all that you have done is "to find the potential answer".

At Brilliant, in the solutions, we ask you to go one step further, and demonstrate that you have indeed found the correct answer. For example "I randomly tried 210 and you told me I was correct" is not a valid solution.

It would be unfortunate if, as a result of having to cram for the JEE, one loses the rigor that is required in mathematics.

Calvin Lin Staff - 6 years, 4 months ago

yeah,I forgot that is to find the total number by adding both numbers but product is the multiplication of two numbers.

Frankie Fook - 6 years, 4 months ago

Aljun Bulado
Feb 9, 2015

(x+1)^2-x^2=29

x^2+2x+1-x^2=29

2x+1=29

x=14

x(x+1)=14(14+1)=210

Good start.

You made a slight assumption that the "larger" square is (x+1)^2, which may not be the case. In this problem, the integers -15, -14 also satisfy the conditions. They do have the same product, since the negative signs cancel out.

Chung Kevin - 6 years, 4 months ago

Difference of 2 squares

2 solutions

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