Question

ma ajutati?1.a).determinati nr nat x,astfel incat x+7 supra3=x+4 supra 2
b)determinati nr nat x,astfel incat x supra 3=4 supra x+1
c)determinati nr nat a si b,astfel incat a supra 5=1 supra b+1
d)determinati nr nat n,astfel incat 2 la puterea n+1 supra 9=8 supra 3 la puterea n
e).determinati nr nat n,astfel incat 5 la puterea n supra 13 la puterea n=7 la puterea n supra 11 la puterea n.
2.aratati ca daca a supra 3=b supra 2 atunci(14a-21b+1)la puterea 2013=1.repede!!cat mai repede!!dau coroana!!AJUTOR!!AJUTATI-MA!!VAA ROGG!!PLS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer 1

1.) a.) 2(x+7)=3(x+4)⇒2x+14=3x+12⇒2x-3x=-14+12⇒-x=-2⇒x=2
b.) x(x+1)=12⇒x²+x=12⇒x²=12-x⇒x=3.
c.) a(b+1)=5⇒a*b+a=5⇒a*b=5-a⇒a=1 si b=4
d.) 9=3² si 8=2³ ⇒ n=2
e.) $5^{n} * 11^{n} = 7^{n} * 13^{n}$⇒n=2

2.) 2a=3b ⇒b=$\frac{2}{3}a$ si a =$\frac{3}{2} b$
Daca inlocuim a cu b in 14a-21b⇒14*3/2b=21b ⇒
$( 21b-21b+1)^{2013}$=1⇒$1^{2013}$=1