Rationalize 7-√3÷7+√3
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Answer:
= 52 - 14√3
_______
46
= 26 - 7√3
_______
23
Step-by-step explanation:
= 7 - √3
_____
7 + √3
= 7 - √3 7 - √3
_____ × _____
7 + √3 7 - √3
= (7 - √3)²
________
(7)² - (√3)²
= (7)² - 2(7)(√3) + (√3)²
________________
49 - 3
= 49 - 14√3 + 3
__________
46
= 49 + 3 - 14√3
__________
46
= 52 - 14√3
_______
46
= 52 14√3
__ - ____
46 46
= 26 7√3
__ - ____
23 23
= 26 - 7√3
_______
23
Identities Used :
(a + b)(a - b) = a² - b²
(a - b)² = a² - 2ab + b²
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