Question

The sum of two numbers is 17 and their product is 70

Answer 1

Given info -

Sum of two numbers is 17 and their product is 70.

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With this information we'll find those two numbers.

Let the number be k and second number be 17 - k

So,

• k (17 - k) = 70

We'll solve this equation. Then a quadratic equation will be formed.

Now

⇒ k (17 - k) = 70

⇒ 17k - k² = 70

⇒ 17k - k² - 70 = 0

Multiply throughout equation by "-"

⇒ - 17k + k² + 70 = 0

Now, rearrange these terms

⇒ k² - 17k + 70 = 0

A quadratic equation has been formed

⇒ k² - 10k - 7k + 70 = 0

Now take common from these terms

⇒ k (k - 10) - 7 (k - 10) = 0

⇒ (k - 7) (k - 10) = 0

Now, equate these two with 0 separately.

⇒ k - 7 = 0

⇒ k = 7

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⇒ k - 10 = 0

⇒ k = 10

Hence, the two numbers are 7 and 10 respectively.