Question

Given that (2 + √3)(√7 + √5) + (2 − √3)(√7 − √5) ≡ a√b + c√d, where a, b, c, and d are integers. Find the values of a, b, c, and d.

a) a = 4, b = 105, c = 0, d = 2
b) a = 4, b = 15, c = 4, d = 35
c) a = 4, b = 105, c = 4, d = 35
d) a = 4, b = 15, c = 0, d = 2

Answer 1

To find the values of a, b, c, and d, expand the given expression and compare it to the given form. In this case, a = 4, b = 7, c = 0, and d = 15.

Step-by-step explanation:

To find the values of a, b, c, and d, we need to expand the given expression and then compare it to the given form a√b + c√d. Let's expand:

(2 + √3)(√7 + √5) + (2 − √3)(√7 − √5)

Using the FOIL method, we get:

2√7 + 2√5 + √21 + √15 + 2√7 - 2√5 - √21 + √15

Simplifying, we can combine like terms:

4√7 + √15 - √21

Comparing it with the given form a√b + c√d, we can see that a = 4, b = 7, c = 0, and d = 15.

Answer 2

The values of a is a) a = 4, b = 15, c = 4, d = 35

Step-by-step explanation:

To find the values of a, b, c, and d in the given expression (2 + √3)(√7 + √5) + (2 − √3)(√7 − √5), we can start by expanding the expression using the distributive property. After expanding and simplifying the expression, we get (2√7 + 2√5 + 3√7 + 3√5) + (2√7 - 2√5 - 3√7 + 3√5). This simplifies further to (5√7 + 5√5) + (-√7 + √5). Combining like terms gives us 4√7 + 4√5.

Therefore, the values of a, b, c, and d are a = 4, b = 15, c = 4, and d = 35. This means that when simplified, the given expression is equivalent to 4√15 + 4√35.

In conclusion, after expanding and simplifying the given expression, we find that the values of a, b, c, and d are a = 4, b = 15, c = 4, and d = 35.

So correct option is opiton a) a = 4, b = 15, c = 4, d = 35