Question

If P=7x² + 5xy - 9y²,Q= 4y² - 3x² - 6xy and R= - 4x² + xy + 5y²

Show that P + Q +R =0​

Answer 1

Given :-

• P = 7x² + 5xy - 9y²
• Q = 4y² - 3x² - 6xy
• R = -4x² + xy + 5y²

To Show :-

• P + Q + R = 0

SoluTion :-

Add P , Q and R.

RHS :-

• 7x² + 5xy - 9y² + (4y² - 3x² - 6xy) + (-4x² + xy + 5y²)

→ 7x² + 5xy - 9y² + 4y² - 3x² - 6xy - 4x² + xy + 5y²

→ 7x² - 3x² - 4x² - 9y² + 4y² + 5y² + 5xy - 6xy + xy

[ re arrange the like terms ]

→ 4x² - 4x² - 9y² + 9y² + 5xy - 5xy

→ 0 = LHS

Hence, P + Q + R = 0

ProVed.

_____________________

Answer 2

It is given that,

• P = (7x² + 5xy - 9y²)
• Q = (4y² - 3x² - 6xy)
• R = (- 4x² + xy + 5y²)

We have to prove that,

P + Q + R = 0

LHS:-

P + Q + R

= (7x² + 5xy - 9y²) + (4y² - 3x² - 6xy) + (- 4x² + xy + 5y²)

= 7x² + 5xy - 9y² + 4y² - 3x² - 6xy - 4x² + xy + 5y²

= 7x² - 3x² - 4x² - 9y² + 4y² + 5y² - 6xy + 5xy + xy

= 7x² - 7x² - 9y² + 9y² - 6xy + 6xy

= 0

RHS:-

0

Thus,

LHS = RHS

Hence, Proved.