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Ex 27 punctele a),b) si c) ...dau coroana

Ex 27 Punctele Ab Si C Dau Coroana class=

Răspuns :

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Vezi imaginea ANNA12
x+1/x=2
a)(x+1/x)²=4
x²+1/x²=4-2=>x²+1/x²=2

b)(x+1/x)³=8
x³+3x+3/x+1/x³=8
x³+1/x³=8-3(x+1/x)
x³+1/x³=8-6=>x³+1/x³=2

c)(x+1/x)⁴=16
(x²+2+1/x²)(x²+2+1/x²)=16
x⁴+2x²+1+2x²+4+2/x²+1+2/x²+1/x⁴=16
x⁴+1/x⁴=16-6-4(x²+1/x²)
x⁴+1/x⁴=10-4·2=>x⁴+1/x⁴=2