Question

If possible help me in this. I need to find the two odd numbers...​

Answer 1

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

Answer: x+2

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Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

Answer: x^2 + (x+2)^2 = 394

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Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(2)\pm√((2)^2-4(1)(-195)))/(2(1))\\\\x = (-2\pm√(784))/(2)\\\\x = (-2\pm28)/(2)\\\\x = (-2+28)/(2) \ \text{ or } \ x = (-2-28)/(2)\\\\x = (26)/(2) \ \text{ or } \ x = (-30)/(2)\\\\x = 13 \ \text{ or } \ x = -15\\\\`

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

Answer: Either 13, 15 or -15, -13