Question

Solve
By Quadratic Formula
(a+b) x + ( a + b + c) x + (b + c)=0​

Answer 1

Answer:

$\star\:\:\bf\large\underline\blue{Question:-}$⋆

Question:−

Simplify the problem.

$\star\:\:\bf\large\underline\blue{Solution:-}$⋆

Solution:−

$\sqrt{a + b + 2x + 2 \sqrt{ab + (a + b)x + {x}^{2} } }$

Now, let

y = $\sqrt{ab + (a + b)x + {x}^{2} }$y=

Therefore,

$\sqrt{a + b + 2x + 2 \sqrt{ab + (a + b)x + {x}^{2} } }$

= $\sqrt{a + b + 2x + 2 + 2 \sqrt{y} }$=

Now, we will factorise y.

$\sqrt{ab + (a + b)x + {x}^{2} }$

= $\sqrt{ab + ax + bx + {x}^{2} }$=

= $\sqrt{a(b + x) +x(b+ x)}$=

= $\sqrt{(x + a)(x + b)}$=

Now,

= $\sqrt{a + b + 2x + 2 + 2 \sqrt{y} }$=

= $\small\sqrt{(x + a) + (x + b) + 2 \sqrt{(x + a)(x + b)} }$=

= $\sqrt{ {( \sqrt{x + a}) }^{2} + {( \sqrt{(x + b} )}^{2} + 2 \times \sqrt{(x + a} \times \sqrt{(x + b)} }$=

= $\sqrt{ {( \sqrt{x + a} + \sqrt{x + b} )}^{2} }$=

= $\sqrt{x + a} + \sqrt{x + b}$=

$\star\:\:\bf\large\underline\blue{Answer:-}$⋆

$\sqrt{x + a } + \sqrt{x + b}$

Answer 2

Answer:

⇒ The given quadratic equation is abx

2

+(b

2

−ac)x−bc=0, aomparing it with Ax

2

+Bx+C=0

⇒ We get, A=ab,B=(b

2

−ac),C=bc

⇒ x=

2A

−B±

B

2

−4AC

=

2(ab)

−(b

2

−ac)±

(b

2

−ac)

2

−4(ab)(−bc)

=

2ab

−b

2

+ac±

b

4

−2b

2

ac+a

2

c

2

+4b

2

ac

=

2ab

−b

2

+ac±

b

4

+2b

2

ac+a

2

c

2

=

2ac

−b

2

+ac±

(b

2

+ac)

2

=

2ac

−b

2

+ac±(b

2

+ac)

⇒ x=

2ac

−b

2

+ac+b

2

+ac

and x=

2ac

−b

2

+ac−b

2

−ac

⇒ x=

2ac

2ac

and x=

2ac

−2b

2

∴ x=2 and x=

ac

−b

2