Question

Express the following expressions as perfect square.
4m²+4+1/m²​

Answer 1

Answer:

$\huge\underbrace\mathbb\pink{Answer~}$

It is given that the equation x

2

−(5m−2)x+(4m

2

+10m+25)=0 is a perfect square. This implies the discriminant D=b

2

−4ac must be equal to 0. Therefore, we have:

D=(5m−2)²−4(4m²+10m+25)

⇒0=[(5m)²+2²−(2×5m×2)]−16m²−40m−100(∵(a−b)

2

=a

2

+b

2

−2ab)

⇒0=25m²+4−20m−16m²−40m−100

⇒0=9m²−60m−96

⇒3(3m²−20m−32)=0

⇒3m²−20m−32=0

Now, we factorize the equation 3m²−20m−32=0 as shown below:

m=

2×3

−(−20)±

(−20)

2

−(4×3×−32)

=

6

20±

400+384

=

6

20±

784

=

6

20±28

=

6

20+28

,

6

20−28

=

6

48

,−

6

8

=8,−

3

4

Hence, m=8 or −

3

4

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