Option d:
[tex](3-\sqrt{5})(2+3 \sqrt{5})=-7+7\sqrt{5}[/tex]
Solution:
Given expression:
[tex](3-\sqrt{5})(2+3 \sqrt{5})[/tex]
To solve this expression.
[tex](3-\sqrt{5})(2+3 \sqrt{5})[/tex]
Multiply each of 1st term into each of 2nd term.
[tex]=3\cdot(2+3 \sqrt{5}) -\sqrt{5} \cdot(2+3 \sqrt{5})[/tex]
[tex]$=3 \cdot 2+3 \cdot 3 \sqrt{5}+(-\sqrt{5}) \cdot 2+(-\sqrt{5}) \cdot 3 \sqrt{5}[/tex]
Apply minus plus rules: [tex]+(-a)=-a[/tex]
[tex]=3 \cdot 2+3 \cdot 3 \sqrt{5}-2 \sqrt{5}-3 \sqrt{5} \sqrt{5}[/tex]
[tex]=6+9\sqrt{5}-2 \sqrt{5}-3 \times 5[/tex]
[tex]=6+9\sqrt{5}-2 \sqrt{5}-15[/tex]
[tex]=-7+7\sqrt{5}[/tex]
[tex](3-\sqrt{5})(2+3 \sqrt{5})=-7+7\sqrt{5}[/tex]
Therefore option d is the correct answer.
