Réponse :
√[(4+√7)/(4-√7)] + √[(4-√7)/(4+√7)]
=√[(4+√7)(4+√7)/(4-√7)(4-√7)] + √[(4-√7)(4-√7)/(4+√7)(4+√7)]
= √[(4+√7)²/9] + √[(4-√7)²/9]
= (4+√7)/3 + (4 - √7)/3
= (4 + √7 + 4 - √7)/3
= 8/3
Explications étape par étape :
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Réponse :
√[(4+√7)/(4-√7)] + √[(4-√7)/(4+√7)]
=√[(4+√7)(4+√7)/(4-√7)(4-√7)] + √[(4-√7)(4-√7)/(4+√7)(4+√7)]
= √[(4+√7)²/9] + √[(4-√7)²/9]
= (4+√7)/3 + (4 - √7)/3
= (4 + √7 + 4 - √7)/3
= 8/3
Explications étape par étape :