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3 years ago

13

The number 2017 can be expressed as the difference of the squares of two consecutive whole numbers. What is the sum of these two

numbers?

1 answer:

SSSSS [86.1K]3 years ago

8 0

Let x be the first number

X + 1 be the second number

So

(x+1)^2 – x^2 = 2017

X^2 + 2x +1 – x^2 = 2017

2x + 1 = 2017

2x = 2017 – 1

2x = 2016

X = 1008

X + 1 = 1009

Sum = 1008 + 1009 = 2017

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I need help with this problem

Soloha48 [4]

Answer:

$3.\ \dfrac{3x}{11x}, \dfrac{6}{22}, \dfrac{9}{33},\dfrac{12}{44}$

$4. -18\\5.\ 400$

Step-by-step explanation:

<u>Solution 3:</u>

Equivalent fractions to are to $\frac{3}{11}$ be found out.

<u>Method: </u> By Multiplying both the denominator and numerator with the same number, we can easily find equivalent fractions.

1. Multiply with 2:

$\dfrac{3 \times 2}{11 \times 2}\\\Rightarrow \dfrac{6}{22}$

2. Multiply with 3:

$\dfrac{3 \times 3}{11 \times 3}\\\Rightarrow \dfrac{9}{33}$

3. Multiply with 4:

$\dfrac{3 \times 4}{11 \times 4}\\\Rightarrow \dfrac{12}{44}$

If we try to write in variable form, it can be written as:

$\dfrac{3x}{11x}$

where x is any number.

---------------

<u>Solution 4:</u>

$(2x-10)$ when $x=-4$

$2 \times (-4) -10\\\Rightarrow -8 -10\\\Rightarrow -18$

------------

<u>Solution 5:</u>

$(10a)^2, a=-2\\\Rightarrow \{10 \times (-2)\}^2\\\Rightarrow (-20)^2\\\Rightarrow 400$

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