If x,y,z are in AP . Prove that (x+2y-z)(2y+z-x)(z+x-y)=4xyz
Suraj Sharma , 7 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> If x,y,z are in AP . Prove that (x+2y-z)(...
2 Answers
Harshit Panwar
Last Activity: 7 Years ago
Since x,y,z are in AP.
Therefore,
d=y-x=z-y=(z-x)/2
(x+2y-z)=x+y+y-z=x+y-(z-y)=x+y-(y-x)=x+y-y+x = 2x
(2y+z-x)=2y+2z-2y =2z. { (z-x)/2=z-y => z-x=2z-2y }
(z+x-y)=z-(y-x)=z-(z-y)=z-z+y =y
(x+2y-z)(2y+z-x)(z+x-y)=2x × 2z × y=4xyz
Hence proved.
ARKADEEP DAS
Last Activity: 7 Years ago
hi suraj
this is typical application of ideas
take x as starter of the series and common difference to be d
then y=x+d
z=x+2d
therefore (x+2y-z)=(x+2x+2d-x-2d)=2x
(2y+z-x)=(2x+2d+x+2d-x)=2(x+2d)=2z
(z+x-y)=(x+2d+x-x-d)=y
so product gives u 4xyz
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Magical Mathematics[Interesting Approach]
Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R
Magical Mathematics[Interesting Approach]
1 Answer Available
Last Activity: 1 Year ago(s)
9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?
Magical Mathematics[Interesting Approach]
1 Answer Available
Last Activity: 2 Year ago(s)
In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?
Magical Mathematics[Interesting Approach]
0 Answer Available
Last Activity: 2 Year ago(s)
for any two sets A and B (A-B)U(B-A)U (A intersection B)
Magical Mathematics[Interesting Approach]
0 Answer Available
Last Activity: 2 Year ago(s)
If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in30:70
Magical Mathematics[Interesting Approach]
0 Answer Available
Last Activity: 2 Year ago(s)