Question

Fie A ( 2 ; 3 ) si B ( 4 ; x ) . Determinati x € R , astfel incat AB = 2V5.​

Answer 1

Răspuns:

Explicație pas cu pas:

Fie A ( 2 ; 3 ) si B ( 4 ; x ) . Determinati x € R , astfel incat AB = 2V5.​

AB=√[(x2-x1)²+(y2-y1)²]   ⇒2√5=√[(4-2)²+(x-3)²]  ⇒2√5=√2²+(x-3)²  ⇒20=4+(x-3)²  ⇒16=x²-6x+9  ⇒x²-6x-7=0  ⇒

Δ=(-6)²-4·1·(-7)=36+28=64  ⇒√Δ=√64=8

X1,2=(6±8)/2  ⇒X1=(6+8)/2=7    X2=(6-8)/2=-1    X1=7   X2=-1

Proba: A(2;3)  B(4;7)  ⇒AB=√[(4-2)²+(7-3)²]=√(2²+4²)=√20=2√5

Proba: A(2;3)  B(4;-1)  ⇒AB=√[(4-2)²+(-1-3)²]=√[(2²+(-4)²]=√20=2√5

Answer 2

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