Answer:
(3 + √2)(3 - √2) = 7 ⇒ answer (c)
Step-by-step explanation:
* Lets study the question
- It is a multiplication of two conjugate binomials
- The meaning of conjugate is two binomials have same numbers
with different middle sign ( sum and difference of 2 terms)
- Their product is a difference of two squares
Ex: (a - b) and (a + b)
∵ (a - b)(a + b) = a × a + a × b + (-b) × a + (-b) × b
∴ (a - b)(a + b) = a² + ab - ab - b² ⇒ ab - ab = 0
∴ (a - b)(a + b) = a² - b²
* Lets do that with our question
∵ (3 + √2)(3 - √2) = 3 × 3 + 3 × -√2 + √2 × 3 + √2 × -√2
∵ √2 × -√2 = -2
∴ (3 + √2)(3 - √2) = 9 - 3√2 + 3√2 - 2 ⇒ -3√2 + 3√2 = 0
∴ (3 + √2)(3 - √2) = 9 - 2 = 7
* The answer is (c)
