Question

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

Answer 1

`\boxed{1}` ✅

`\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}`

`(7 + 4 √(3) ) \: (7 - 4 √(3) ) \\ \\ = 7 \: (7 - 4 √(3) ) + 4 √(3) (7 - 4 √(3) ) \\ \\ = 49 - 28 √(3) + 28 √(3) - 48 \: (since \: √(3) * √(3) = 3)\\ \\ = 49 - 48 \\ \\ = 1`

You can also use the identity:

( a + b ) ( a - b ) =
`{a}^(2) - {b}^(2)`

`\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}`

Answer 2

Explanation:

(a + b)(a - b) = a² - b²

`(7 + 4√(3)) (7 - 4√(3)) = 7^(2)-(4√(3) )^(2)\\\\ = 49 - 4^(2)*(√(3))^(2)\\\\= 49 - 16 * 3\\\\= 49 - 48\\\\= 1`