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zmlpnhlths
@zmlpnhlths
July 2022
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Решите, пожалуйста, если можно подробно и желательно сегодня)
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sangers1959
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1. ab⁻¹+a⁻¹b+1=a/b+b/a+1=(a²+b²+ab)/ab=(a²+ab+b²)/ab.
2. (a⁻¹-b⁻¹)²=(1/a-1/b)²=1/a²-2/ab+1/b²=(b²-2ab+a²)/a²b²=(a-b)²/a²b².
3. a²b⁻²+a⁻²b²=a²/b²+b²/a²=(a⁴+b⁴)/a²b².
4. ab⁻¹+a⁻¹b=a/b+b/a=(a²+b²)/ab.
5. (a⁴+b⁴)/a²b²-(a²+b²)/ab=(a⁴+b⁴-ab(a²+b²))/a²b²=(a⁴+b⁴-a³b-ab³)/a²b²=
=(a³(a-b)-b³(a-b))/a²b²=(a³-b³)(a-b)/a²b²=(a-b)(a²+ab+b²)(a-b)/a²b²=
=(a²+ab+b²)(a-b)²/a²b².
6. (a²+ab+b²)(a-b)²*a²b²/((a²+ab+b²)(a-b)²*a²b²*ab)=1/ab=1/(4*5)=1/20.
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zmlpnhlths
спасибо огромное))
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Verified answer
1. ab⁻¹+a⁻¹b+1=a/b+b/a+1=(a²+b²+ab)/ab=(a²+ab+b²)/ab.2. (a⁻¹-b⁻¹)²=(1/a-1/b)²=1/a²-2/ab+1/b²=(b²-2ab+a²)/a²b²=(a-b)²/a²b².
3. a²b⁻²+a⁻²b²=a²/b²+b²/a²=(a⁴+b⁴)/a²b².
4. ab⁻¹+a⁻¹b=a/b+b/a=(a²+b²)/ab.
5. (a⁴+b⁴)/a²b²-(a²+b²)/ab=(a⁴+b⁴-ab(a²+b²))/a²b²=(a⁴+b⁴-a³b-ab³)/a²b²=
=(a³(a-b)-b³(a-b))/a²b²=(a³-b³)(a-b)/a²b²=(a-b)(a²+ab+b²)(a-b)/a²b²=
=(a²+ab+b²)(a-b)²/a²b².
6. (a²+ab+b²)(a-b)²*a²b²/((a²+ab+b²)(a-b)²*a²b²*ab)=1/ab=1/(4*5)=1/20.