Description
Q.1. m^4 + 3m^2 + 4
Q.2. y^4 + 2y^2 + 9
Q.3. (2x+y)^2 - z^2
Q.4. 4y^4 - 16y^2 + 9
Q.5. m^2 + 6m + 9 - 4n^2
Q.6. 16y^2 - a^2 - 6ab - 9b^2
Explanation & Answer
Q.1. m^4 + 3m^2 + 4
= (m^2)^2 + 3m^2 + 4
Now a = 1 b = 3 c= 4 , then
m^2 = (-b ± √b^2 - 4ac)/2a
Now
= (-3 ± √(3)^2 - 4(1)(4))/2(1)
= (- 3 ± √9 - 16)/2
= (- 3 ± √-7)/2
m^2 = (- 3 ± 7i)/2
Hence m = √(- 3 ± 7i)/2
Q.2. y^4 + 2y^2 + 9
(y^2)^2 + 2y^2 + 9
a = 1 b = 2 c = 9
y^2 = (-b ± √b^2 - 4ac)/2a
Now
= (-(2) ± √(2)^2 - 4(1)(9))/2(1)
= (-2 ± √4 - 36)/2
= (-2 ± √- 32)/2
= (-2 ± √- 8 * 4)/2
= (-2 ± 2√- 8)/2= 2(-1 ± √-8)/2
= (-1 ± 8i)
y^2 = (-1 ± 8i)
Hence y = √(-1 ± 8i)
Q.3. (2x+y)^2 - z^2
(2x+y)^2 - z^2
= (2x+y - z)(2x + y + z) As a^2 - b^2 = (a - b)(a + b)
Q.4. 4y^4 - 16y^2 + 9
4(y^2)^2 - 16y^2 + 9
a = 4 b = -16 c = 9
Now
y^2 = (-b ± √b^2 - 4ac)/2a
= (-(-16) ± √(-16)^2 - 4(4)(9))/2(4)
= (16 ± √256 - 144)/8
= (16 ± √112)/8
= (16 ± √16 * 7)/8
= (16 ± 4√7)/8
= 4(4 ± √7)/8
= (4 ± √7)/2
y ^2 = (4 ± √7)/2
Hence y = √(4 ± √7)/2
Q.5. m^2 + 6m + 9 - 4n^2
= m^2 + 3m + 3m + 9 - 4n^2
= m(m + 3) + 3(m + 3) - 4n^2
= (m + 3)(m + 3) - 4n^2
= (m + 3)^2 - 4n^2
= (m + 3)^2 - (2n)^2
= (m + 3 - 2n)(m + 3 + 2n) As a^2 - b^2 = (a - b)(a + b)
Q.6. 16y^2 - a^2 - 6ab - 9b^2
= 16y^2 - a^2 - 2*3*ab - 9b^2
= 16y^2 - (a^2 + 2*3*ab + 9b^2)
= 16y^2 - ((a)^2 + 2*3*ab + (3b)^2)
= 16y^2 - (a + 3b)^2 As a^2 + 2ab + b^2 = (a + b)^2
= (4y)^2 - (a + 3b)^2
= (4y - a + 3b)(4y + a + 3b) As a^2 - b^2 = (a - b)(a + b)