(Ip) 5. Comparați numerele raţionale pozitive ​

[tex]x = (1 - ( \frac{3}{10} + \frac{8}{15} ) \times \frac{12}{25} )^{2} \\ x = (1 - ( \frac{3 \times 3}{10 \times 3} + \frac{8 \times 2}{15 \times 2} ) \times \frac{12}{25} )^{2} \\ x = (1 - \frac{9 + 18}{30} \times \frac{12}{25} )^{2} \\ x = (1 - \frac{27}{30} \times \frac{12}{25} ) ^{2} \\ x = (1 - \frac{9}{10} \times \frac{12}{25} ) ^{2} \\ x = (1 - \frac{9 \times 12}{10 \times 25} )^{2} \\ x = (1 - \frac{9 \times 6}{5 \times 25} )^{2} \\ x = (1 - \frac{54}{125} )^{2} \\ x = ( \frac{125 - 54}{125} )^{2} \\ x = ( \frac{71}{125} ) ^{2}x = \frac{71 \times 71}{125 \times 125} \\ x = \frac{5041}{15625} [/tex]

asadar, avem de comparat 2/5 cu 5041/15625

aducem la acelasi numitor

[tex]x = \frac{5041}{15625} \: \: \: y = \frac{2}{5} \\ x = \frac{5041}{15625} \: \: \: \: y = \frac{3125 \times 2}{15625} \\ x = \frac{5041}{15625} \: \: \: y = \frac{6250}{15625} [/tex]

deci y este mai mare (al doilea numar)

Răspuns:

x=[1-(3/10+8/15)*12/25]2

=[1-(3*3+8*2)/30*12/25]^2

=[1-(25/30*12/25)]^2

=[1-2/5]^2=3/5^2=9/25

fie y=2/5=10/25

10/25>9/25

y>x