hamburger menu
All Coursesall course arrow
adda247
reward-icon
adda247
    arrow
    arrow
    arrow
    The value of p2−(q−r)2(p+r)2−q2+q2−(p−r)2(p+q)2−r2+r2−(p−q)2(q+r)2−p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 -
    Question

    The value of p2(qr)2(p+r)2q2+q2(pr)2(p+q)2r2+r2(pq)2(q+r)2p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2} is​

    A.

    1

    B.

    2

    C.

    0

    D.

    3

    Correct option is A

    Given: 
    p2(qr)2(p+r)2q2+q2(pr)2(p+q)2r2+r2(pq)2(q+r)2p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2} 
    Concept Used: 
    We can find the value of the expression by letting the values of p, q and r.
    Solution: 
    Putting p = q = r = 1
    p2(qr)2(p+r)2q2+q2(pr)2(p+q)2r2+r2(pq)2(q+r)2p2\frac{p^2 - (q - r)^2}{(p + r)^2 - q^2} + \frac{q^2 - (p - r)^2}{(p + q)^2 - r^2} + \frac{r^2 - (p - q)^2}{(q + r)^2 - p^2}

    12(11)2(1+1)212+12(11)2(1+1)212+12(11)2(1+1)212\frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2} + \frac{1^2 - (1 - 1)^2}{(1 + 1)^2 - 1^2}
    =13+13+13\frac{1}{3}+\frac{1}{3}+\frac{1}{3}
    = 1
    Thus, the value of the expression is 1. 

    Free Tests

    Free
    Must Attempt

    SSC GD PYP (Held on 4 Feb 2025 S1)

    languageIcon English
    • pdpQsnIcon80 Questions
    • pdpsheetsIcon160 Marks
    • timerIcon60 Mins
    languageIcon English
    Free
    Must Attempt

    Hindi Section Test 1

    languageIcon English
    • pdpQsnIcon20 Questions
    • pdpsheetsIcon40 Marks
    • timerIcon12 Mins
    languageIcon English
    Free
    Must Attempt

    SSC GD Constable Full Mock Test 1

    languageIcon English
    • pdpQsnIcon80 Questions
    • pdpsheetsIcon160 Marks
    • timerIcon60 Mins
    languageIcon English
    test-prime-package

    Access ‘SSC CGL Tier I’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    students-icon
    368k+ students have already unlocked exclusive benefits with Test Prime!
    Our Plans
    Monthsup-arrow