rachelachu05
Answered

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the value of ( 7 + 4root 3) ( 7 - 4 root 3) is​

Sagot :

devishri1977

Answer:

Step-by-step explanation:

(a + b)(a - b) = a² - b²

[tex](7 + 4\sqrt{3}) (7 - 4\sqrt{3}) = 7^{2}-(4\sqrt{3} )^{2}\\\\ = 49 - 4^{2}*(\sqrt{3})^{2}\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1[/tex]

[tex]\boxed{1}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex](7 + 4 \sqrt{3} ) \: (7 - 4 \sqrt{3} ) \\ \\ = 7 \: (7 - 4 \sqrt{3} ) + 4 \sqrt{3} (7 - 4 \sqrt{3} ) \\ \\ = 49 - 28 \sqrt{3} + 28 \sqrt{3} - 48 \: (since \: \sqrt{3} \times \sqrt{3} = 3)\\ \\ = 49 - 48 \\ \\ = 1[/tex]

You can also use the identity:

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

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