Question

If p = -2, q = -1 , r = 3 , find the value of : a) p 2 + q 2 – r 2 b) 2p 2 – q 2 + 3r
please solve

Answer 1

Answer:

RQ=RP

⇒∠ROP=∠RPQ=x      [∵ Angle opposite to equal side is equal]

Now,

∠RPQ=50  

o

     [Vertically opposite angles]

∴x=50  *

Step-by-step explanation:

a) STEP

1

:

Equation at the end of step 1

 ((p2)-((2•(q2))•r))•(2p2-3r)

STEP  

2

:

Equation at the end of step

2

:

 ((p2) -  (2q2 • r)) • (2p2 - 3r)

STEP

3

:

Trying to factor as a Difference of Squares

3.1      Factoring:  p2-2q2r  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

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