Question

Rezolvati in R urmatoarele ecuatii:

(x-√2)²-1=17
(4x-5√5)²+83=128
(3√7-2x)²-75=100

Answer 1

a)(x-√2)²-1=17⇒(x²-2√2x+2)-1=17⇒x²-2√2x+2-17-1=0⇒x²-2√2x-16=0
a=1
b=2√2
c=-16
Δ=b²-4ac⇒Δ=(2√2)²-4×1×(-16)⇒Δ=8+64⇒Δ=72⇒Δ=6√2
x1x2=-b+-√Δ/2a⇒
x1=-2√2+6√2/2⇒4√2/2=2√2
x2=-2√2-6√2/2⇒-8√2/2=-4√2

b)(3√7-2x)²-75=100⇒(9×7-6√7x+4x²)-75=100⇒
63-6√7x+4x²-75-100=0⇒4x²-6√7x-112=0
a=4
b=-6√7
c=-112
Δ=b²-4ac⇒Δ=(-6√7)²-4×4×(-112)⇒Δ=252+1792⇒Δ=2044⇒√Δ=√2044⇒Δ=
nu imi iese delta?