# i. Let’s write for which value of t, will be a whole square form.ii. Let’s write the expression which when added to gives a whole square.iii. If a and b are positive integers and lets write the value of a & b.iv. an identity or an equation? Write with reason.v. For each positive or negative value of x and y except zero the value of is always (positive or negative)

i. For making a complete square, we need to reduce the expression in x2± 2xy + y2form, so if we put t = ±1, then we get expression as

Hence, for t = ±1, the given equation will be a whole square form.

ii. For making a complete square, we need to reduce the expression in x2 + 2xy + y2form, so if we add ±4x to given equation, we have

a2 + 4 ± 4x

= a2± 4x + 4

= a2± 2(2)x + 22

= (a ± 2)2

Hence, if we add 4x to the given expression, the expression becomes a whole square.

iii. Given,

a2 – b2 = 9 × 11

we know, a2 – b2 = (a - b)(a + b)

(a – b)(a + b) = 9 × 11

On comparison, we get

a – b = 9 [1]

a + b = 11 [2]

a + b + a – b = 9 + 11

2a = 20

a = 10

Putting value of ‘a’ in equation [1], we get

10 – b = 9

b = 10 – 9

b = 1

iv. Identity, as

Taking LHS

Now, we know

(x + y)2 = x2 + 2xy + y2

and (x – y)2 = x2 – 2xy + y2

Applying above identities in LHS, we get

= (x + y)2 – (x – y)2

= x2 + 2xy + y2 – (x2 – 2xy + y2)

= x2 + 2xy + y2 – x2 + 2xy – y2

= 4xy

= RHS

As, LHS = RHS the given expression is an identity!

v. Square of any number is always positive

[Explanation: Suppose -a (a > 0) is a negative number, then

(-a)2 = -a × (-a) = a2]

Therefore, a2and b2 both are positive numbers

a2 + b2 is a positive number, as sum of two positive numbers is positive!

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