Toán Lớp 9: a√ a + b√ b/√ a+√ b – √ ab rút gọn
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Toán Lớp 9: a√ a + b√ b/√ a+√ b – √ ab rút gọn
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= {\sqrt{a}^3 + \sqrt{b}^3}/{\sqrt{a} + \sqrt{b}} – \sqrt{ab}
= {(\sqrt{a} + \sqrt{b})(a – \sqrt{ab} + b)}/{\sqrt{a} + \sqrt{b}} – \sqrt{ab}
= a – \sqrt{ab} + b – \sqrt{ab}
= a – 2\sqrt{ab} + b
= \sqrt{a}^2 – 2\sqrt{a}.\sqrt{b} + \sqrt{b}^2
= (\sqrt{a} – \sqrt{b})^2
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Áp dụng HĐT số 6:$A^3 + B^3 = (A+B)(A^2 – AB + B^2)$
HĐt số 2:$A^2 -2AB + B^2 =(A-B)^2$