Q13 of 84 Page 5

Prove that a2+ b2+c2–ab–bc–ca is always non-negative for all values of a, b and c.

We have to prove that a2+ b2+c2–ab–bc–ca 0

Lets us consider,



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11

If 3x - 7y = 10 and xy = -1, find the value of 9x2 + 49y2

 12

Simplify each of the following products:

(i)


(ii)


(iii) -x2 + 2x


(iv) (x2 + x – 2) (x2 - x + 2)


(v) (x3 - 3x2 – x) (x2 - 3x + 1)


(vi) (2x4 - 4x2 + 1) (2x4 - 4x2 - 1)

 1

Write the following in the expanded form:

(i) (a + 2b + c)2


(ii) (2a - 3b - c)2


(iii) (-3x + y + z)2


(iv) (m + 2n – 5p)2


(v) (2 + x – 2y)2


(vi) (a2 + b2 + c2)2


(vii) (ab + bc + ca)2


(viii)


(ix)


(x) (x + 2y + 4z)2


(xi) (2x - y + z)2


(xii) (-2x + 3y + 2z)2

 2

Simplify:

(i) (a+b+c)2 +(a-b+c)2


(ii) (a+b+c)2 -(a-b+c)2


(iii) (a+b+c)2 +(a-b+c)2+(a+b-c)2


(iv) (2x+p+c)2-(2x-p+c)2


(v) (x2+y2-z2)2-(x2-y2+z2)2