Answer:
option (b) is correct
The product of [tex](7-\sqrt{7} )[/tex] and [tex](-6+\sqrt{7} )[/tex] is [tex]-49+13\sqrt{7}[/tex]
Step-by-step explanation:
Given radicals [tex](7-\sqrt{7} )[/tex] and [tex](-6+\sqrt{7} )[/tex]
WE have to find the product of two given radicals
Consider [tex]\left(7-\sqrt{7}\:\right)\left(-6+\sqrt{7}\:\right)[/tex]
Using property of algebra,
[tex]\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex] , We have ,
[tex]=7\left(-6\right)+7\sqrt{7}+\left(-\sqrt{7}\right)\left(-6\right)+\left(-\sqrt{7}\right)\sqrt{7}[/tex]
Simplifying further , we get,
[tex]=-7\cdot \:6+7\sqrt{7}+6\sqrt{7}-\sqrt{7}\sqrt{7}[/tex]
Adding similar terms , we get,
[tex]=-49+13\sqrt{7}[/tex]
Thus, the product of [tex](7-\sqrt{7} )[/tex] and [tex](-6+\sqrt{7} )[/tex] is [tex]-49+13\sqrt{7}[/tex]
Thus, option (b) is correct
