Home
Class 9
MATHS
If a/b = c/d = e/f, then prove that eac...

If ` a/b = c/d = e/f`, then prove that each of these ratio's is equal to `((4a^(2)+3c^(2)-7e^(2))/(4b^(2)+3d^(2)-7f^(2)))^(1//2)`

Text Solution

Verified by Experts

Let ` a/b = c/d = e/f = k`.
` rArr a = kb, c = kd, e = kf`.
Now, `((4a^(2)+3c^(2)-7e^(2))/((4b^(2)+3d^(2)-7f^(2))))^(1//2) = (((4(kb)^(2)+3(kd)^(2)-7(kf)^(2)))/(4b^(2)+3d^(2)-7f^(2)))^(1//2)`
` =[(k^(2)(4b^(2)+3d^(2)-7f^(2)))/((4b^(2)+3d^(2)-7f^(2)))]^(1//2) = k`.
Hence, proved.
Promotional Banner

Topper's Solved these Questions

  • RATIO, PROPORTION AND VARIATION

    PEARSON IIT JEE FOUNDATION|Exercise Very Short Type Questions|30 Videos

  • RATIO, PROPORTION AND VARIATION

    PEARSON IIT JEE FOUNDATION|Exercise Short Answer Type Questions|15 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 3|23 Videos

  • SALES TAX AND COST OF LIVING INDEX

    PEARSON IIT JEE FOUNDATION|Exercise Level 3|14 Videos

Similar Questions

Explore conceptually related problems

If (a)/(2b) = (c )/(d) = (e )/(3f) , then the value of (2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(32b^(6)+12b^(2)d^(2)-405f^(5)) is

If (a)/(b)=(c)/(d)=(e)/(f)=3 , then (2a^2 + 3c^(2) + 4e^(2))/(2b^(2) + 3d^(2) + 4f^(2))=?

If a/b = c/d =e/f = 4, then (m ^(2) a + n^(2) c + p ^(2) e )/( m ^(2) b + n ^(2) d + p ^(2) f )=?

If a/b=c/d=e/f, then show that (a^(3)b+2c^(2)e-3ae^(2)f)/(b^(4)+2d^(2)f-3bf^(3))=(ace)/(bdf) (wherever defined)

If (a)/(b)=(c)/(d)=(e)/(f), prove that (b^(2)+d^(2)+f^(2))(a^(2)+c^(2)+e^(2))=(ab+cd+ef)^(2)