Question

(√5 - 2√3) * (√5+2√3)  :7

Answer 1

$( \sqrt{5} -2 \sqrt{3} )( \sqrt{5} +2 \sqrt{3} ):7 = ( (\sqrt{5} )^{2} - (2 \sqrt{3} )^{2} ):7 = (5-12):7 = -1$

Answer 2

To simplify the expression (√5 - 2√3) * (√5 + 2√3) ÷ 7, we can use the difference of squares formula:

(a - b)(a + b) = a^2 - b^2.

In this case, let a = √5 and b = 2√3:

(√5 - 2√3)(√5 + 2√3) = (√5)^2 - (2√3)^2.

Simplifying the expression within parentheses:

(√5 - 2√3)(√5 + 2√3) = 5 - 4 * 3.

(√5 - 2√3)(√5 + 2√3) = 5 - 12.

(√5 - 2√3)(√5 + 2√3) = -7.

Now, we divide the result by 7:

-7 ÷ 7 = -1.

Therefore, (√5 - 2√3)(√5 + 2√3) ÷ 7 equals -1.