Question

Given that

10 - V18 = a + bV2 , where a and b are integers.
V2

Find the values of a and b.

Answer 1

The given equation is simplified by expressing square root of 18 in terms of square root of 2, leading to the identification of a as 10 and b as -3.

Step-by-step explanation:

To find the values of a and b in the equation 10 - \(\sqrt{18}\) = a + b\(\sqrt{2}\), we must express \(\sqrt{18}\) in terms of \(\sqrt{2}\). Recall that \(\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}\). Now we substitute \(3\sqrt{2}\) for \(\sqrt{18}\) in the original equation, yielding:

10 - 3\(\sqrt{2}\) = a + b\(\sqrt{2}\)

By comparing the rational and irrational parts separately since they can only be equal if their respective parts are equal, we find that:

• On the rational side: 10 = a
• On the irrational side: -3\(\sqrt{2}\) = b\(\sqrt{2}\)

Thus, we deduce the integer values of a and b are:

• a = 10
• b = -3