Question

Ajutați-mă cu ex. 11 si 12 va rog. R/s la 11 e 120 cm2, la 12 e a = {1/2;1}, dar cum...?

Answer 1

21. a ipotenuza, b,c catetele, b-c=14
a²=b²+c²
dar a=2R=26
a²=b²+c²=b²+c²-2bc+2bc=(b-c)²+2bc
676=196+2bc
2bc=676-196
2bc=482
bc=240
A=bc/2=120 cm²
22. x²-2a(x-1)-1=0
x²-2ax+2a-1=0
relatiile lui Viete
x1+x2=2a
x1x2=2a-1
x1²+x2²=x1+x2=2a
x1²+x2²=x1²+x2²+2x1x2-2x1x2=(x1+x2)²-2x1x2
2a=4a²-2(2a-1)
2a=4a²-4a+2
4a²-6a+2=0
2a²-3a+1=0
2a²-2a-a+1=0
2a(a-1)-(a-1)=0
(a-1)(2a-1)=0
a-1=0, a=1
2a-1=0, a=1/2