(x+1)^2=2(x+1) is a quatratic equation in x
Answers
Answer:
Check whether the following are quadratic equations :
(i) (x+1)
2
=2(x−3)
(ii) x
2
−2x=(−2)(3−x)
(iii) (x−2)(x+1)=(x−1)(x+3)
(iv) (x−3)(2x+1)=x(x+5)
(v) (2x−1)(x−3)=(x+5)(x−1)
(vi) x
2
+3x+1=(x−2)
2
(vii) (x+2)
3
=2x(x
2
−1)
(viii) x
3
−4x
2
−x+1=(x−2)
3
ANSWER
i)
(x+1)
2
=2(x−3)
x
2
+2x+1=2x−6
x
2
+7=0 → Quadratic
ii)
x
2
−2x=−2(3−x)
x
2
−2x=−6+2x
x
2
+4x+6=0 → Quadratic
iii)
(x−2)(x+1)=(x−1)(x+3)
x
2
−x−2=x
2
+2x−3
3x=1 → Non Quadratic
iv)
(x−3)(2x+1)=(x)(x+5)
2x
2
−5x−3=x
2
+5x
x
2
+10x−3=0 → Quadratic
v)
(x−3)(2x−1)=(x−1)(x+5)
2x
2
−7x+3=x
2
+4x−5
x
2
−11x+8=0 → Quadratic
vi)
x
2
+3x+1=(x−2)
2
x
2
+3x+1=x
2
−4x+4
7x=3 → Non Quadratic
vii)
(x+2)
3
=2x(x
2
−1)
x
3
+8+6x(x+2)=2x
3
−2x
x
3
+8+6x
2
+12x=2x
3
−2x
−x
3
+6x
2
+14x+8=0 → Non Quadratic
viii)
x
3
−4x
2
−x+1
=x
3
+3x
2
(−2)+3x(−2)
2
+(−2)
3
x
3
−4x
2
−x+1=x
3
−6x
2
+12x−8
x
3
−4x
2
−x+1−x
3
+6x
2
−12x+8=0
2x
2
−13x+9=0 → Non Quadratic