Question

I used a calculator and have solved it without. I didn't get any of these answers. HELP

Answer 1

Option d:

$(3-\sqrt{5})(2+3 \sqrt{5})=-7+7\sqrt{5}$

Solution:

Given expression:

$(3-\sqrt{5})(2+3 \sqrt{5})$

To solve this expression.

$(3-\sqrt{5})(2+3 \sqrt{5})$

Multiply each of 1st term into each of 2nd term.

         $=3\cdot(2+3 \sqrt{5}) -\sqrt{5} \cdot(2+3 \sqrt{5})$

         $=3 \cdot 2+3 \cdot 3 \sqrt{5}+(-\sqrt{5}) \cdot 2+(-\sqrt{5}) \cdot 3 \sqrt{5}$

Apply minus plus rules: $+(-a)=-a$

         $=3 \cdot 2+3 \cdot 3 \sqrt{5}-2 \sqrt{5}-3 \sqrt{5} \sqrt{5}$

         $=6+9\sqrt{5}-2 \sqrt{5}-3 \times 5$

         $=6+9\sqrt{5}-2 \sqrt{5}-15$

         $=-7+7\sqrt{5}$

$(3-\sqrt{5})(2+3 \sqrt{5})=-7+7\sqrt{5}$

Therefore option d is the correct answer.