Question

If (4 - √(11))² = a + b √(c), state the values of a, b, and c.

a) a = 7, b = 2, c = 11
b) a = 11, b = -8, c = 11
c) a = 16, b = 5, c = 4
d) a = 8, b = 4, c = 7

Answer 1

The expansion of (4 - √(11))² results in 27 - 8√(11), giving values of a = 27, b = -8, and c = 11, which corresponds to option b of the provided choices.

Step-by-step explanation:

To find the values of a, b, and c when expanding the square of the binomial (4 - √(11))², we use the formula for squaring a binomial ((a - b)² = a² - 2ab + b²).

Using the formula, we expand it step by step:

• First, square the first term: 4² = 16.
• Second, multiply the first term by the second term and by -2: 2(4)²(√(11)) = 8√(11).
• Then, square the second term: (√(11))² = 11.

Combining these, we get: 16 - 8√(11) + 11. Now, simply combine like terms to get: 16 + 11 - 8√(11), which simplifies to 27 - 8√(11).

Therefore, in the form a + b√(c), the values are:

• a = 27
• b = -8
• c = 11

The correct values are: a = 27, b = -8, c = 11, which corresponds to option b).