Question

Buna ma ajutati si pe mine la cateva exercitii?
1.
1 supra 60 : ( 1 supra 30) - ( 6 supra 10) = ?
2.
( -2x + 3 )² = ?
( 5 + 3y) ² = ?
( 2xy - 3a ) · ( 2y + a ) = ?
3.
a = √ (2-√5)² (tot sub radical) + √ (2+√5)² (tot sub radical)
b = √ 500
a) Aratati ca a = 2√5
b) mg ( a ; b ) = ?
4. Rezolvati ecuatia: 3x-2 supra 2 - x-4 supra 3 = 5
5. Dupa ce a cheltuit 65% din suma pe care o avea , un elev a ramas cu 175 lei. Aflati suma pe care o avea elevul.

Answer 1

$\displaystyle 1). \frac{1}{60} : \frac{1}{30} - \frac{6}{10} = \frac{1}{60} \cdot 30- \frac{6}{10} = \frac{30}{60} - \frac{6}{10} = \frac{30-36}{60} =- \frac{6}{60} =- \frac{1}{10} \\ \\ 2a).(-2x+3)^2=(2x-3)^2=(2x)^2-2 \cdot 2x \cdot 3+3^2=4x^2-12x+9 \\ \\ b).(5+3y) ^2=5^2+2 \cdot 5 \cdot 3y+(3y)^2=25+30y+9y^2 \\ \\ c).(2xy-3a)(2y+a)=4xy^2+2axy-6ay-3a^2$

$\displaystyle 3).a= \sqrt{(2- \sqrt{5} )^2} + \sqrt{(2+ \sqrt{5} )^2} \\ b= \sqrt{500} \\ a).a= \sqrt{(2- \sqrt{5} )^2} + \sqrt{(2+ \sqrt{5} )^2} \\ a=|2- \sqrt{5} |+|2+ \sqrt{5} | \\ a= \sqrt{5} -2+ \sqrt{5} +2 \\ a= \sqrt{5} + \sqrt{5} \\ a=2 \sqrt{5} \\ b).m_g= \frac{a+b}{2} \\ a=2 \sqrt{5} ~;b= \sqrt{500} =10 \sqrt{5} \\ \\ m_g= \frac{2 \sqrt{5} +10 \sqrt{5} }{2} = \frac{12 \sqrt{5} }{2} =6 \sqrt{5}$

$\displaystyle 4). \frac{3x-2}{2} - \frac{x-4}{3} =5 \\ 3(3x-2)-2(x-4)=5 \cdot 6 \\ 9x-6-2x+8=30 \\ 9x-2x=30+6-8 \\ 7x=28 \\ x= \frac{28}{7} \\ x=4$

$\displaystyle 5). a- \frac{65}{100} \cdot a=175 \\ \\ \frac{100a}{100} - \frac{65a}{100} =175 \\ \\ \frac{35a}{100} =175 \\ \\ 35a=175 \cdot 100 \\ 35a=17500 \\ a=17500:35 \\ a=500$