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Study the example below for the product of conjugate pairs (3 + sqrt(7))(3 - sqrt(7)) =9-3 sqrt 7 +3 sqrt 7 -7 =9-7 =2 Now, find the product (2 + sqrt(5))(2 - sqrt(5)) The product is

Respuesta :

Nevens

Answer:

- 1

Step-by-step explanation:

we need to know that

( a + b ) × ( a - b ) = [tex]a^{2} -b^{2}[/tex]

proof :

( a + b ) × ( a - b )

[tex]=a * a - a * b + a * b - b * b\\ = a * a - b * b\\= a^{2} - b^{2}[/tex]

so the ans is :

[tex]=2^{2} -(\sqrt{5} )^{2} \\=4 - 5\\=-1[/tex]

Cetacea

The product is -1.

We will use the FOIL method to find the product.

[tex]\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)\\=4-2\sqrt{5}+2\sqrt{5}-\left(\sqrt{5}\right)^{2}\\=4-2\sqrt{5}+2\sqrt{5}-5\\=4-5\\=-1[/tex]

The product is -1.

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