Solve (3+sqrt{2})(3-sqrt{2}):7+(sqrt{2})^2=3

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

Verify

Solution Steps

Multiply both sides of the equation by 7.

$$\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)+7\left(\sqrt{2}\right)^{2}=21$$

Consider \left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$9-\left(\sqrt{2}\right)^{2}+7\left(\sqrt{2}\right)^{2}=21$$

The square of \sqrt{2} is 2.

$$9-2+7\left(\sqrt{2}\right)^{2}=21$$

Subtract 2 from 9 to get 7.

$$7+7\left(\sqrt{2}\right)^{2}=21$$

The square of \sqrt{2} is 2.

$$7+7\times 2=21$$

Multiply 7 and 2 to get 14.

$$7+14=21$$

Add 7 and 14 to get 21.

$$21=21$$

Compare 21 and 21.

$$\text{true}$$