Math, asked by poondekdee2009, 10 months ago

find the roots by quadratic formula: 4y^2+4by-(a^2-b^2 )=0

Answers

Answered by amitkumar44481
30

Answer :

a + b / 2 and a - b / 2.

SolutioN :

We have, Quadratic Equation.

 \tt \dagger \:  \:  \:  \:  \: 4 {y}^{2}  + 4by - ( {a}^{2} +  {b}^{2}) = 0.

Compare With General Equation.

 \tt \dagger \:  \:  \:  \:  \: a {x}^{2}  + bx + c = 0.

Where as,

  • a = 4.
  • b = 4b.
  • c = - ( a² - b² )

☛ We know, Quadratic Formula.

 \tt \dagger \:  \:  \:  \:  \:  \boxed{ \tt x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}}

\tt:  \implies y =  \dfrac{ -4y \pm \sqrt{ {(4b)}^{2} - 4 \times 4 \times  - ( {a}^{2}  +  {b}^{2})  } }{2 \times 4}

\tt:  \implies y =  \dfrac{ -4b \pm \sqrt{ {16b}^{2}  + 16 ( {a}^{2}  +  {b}^{2})  } }{2 \times 4}

\tt:  \implies y =  \dfrac{ -4b \pm \sqrt{ {16b}^{2}  + 16  {a}^{2}   -  16 {b}^{2}} }{8}

\tt:  \implies y =  \dfrac{ -4b \pm \sqrt{16{a}^{2}}}{8}

\tt:  \implies y =  \dfrac{ -4b \pm 4a}{8}

Either,

\tt:  \implies y =  \dfrac{ -4b +  4a}{8}

\tt:  \implies y =  \dfrac{ 4a-4b}{8}

\tt:  \implies y =  \dfrac{ 4(a-b)}{8}

\tt:  \implies y =  \dfrac{ a-b}{2}

Or,

\tt:  \implies y =  \dfrac{ -4b  -  4a}{8}

\tt:  \implies y =  \dfrac{ -4(b   +  a)}{8}

\tt:  \implies y =  \dfrac{ a + b}{2}

Therefore, the value of y = a + b / 2 and a - b / 2.


TheMoonlìghtPhoenix: Great!
amitkumar44481: Thanks :-)
Answered by Anonymous
57

QUESTION :

Find the roots by quadratic formula :

4y² + 4by - (a² – b² ) = 0

GIVEN :

  • 4y² + 4by – ( a² + b² ) = 0

TO FIND :

  • The given roots by quadratic formula, when the informations are given = ?

STEP - BY - STEP EXPLAINATION :

→ 4y² + 4by – ( a² + b² ) = 0 ( GIVEN )

→ Formula ( quadratic formula ) =

x = -b + √b² – 4ac / 2a

( substituting the same formula as per the question asked )

→ y = -4y + √ (4b)² – 4×4 × (a² + b²) / 2 × 4

→ y = -4b + √16b² (a² + b²) / 2 × 4

→ y = -4b + √16b² + 16a² – 16b² / 8

→ y = -4b + √16a² / 8

→ y = -4b – 4a /8

→ y = 4 (b + a) / 8

y = a + b / 2

→ y = -4b + 4a /8

→ y = 4a – 4b /8

→ y = 4 (a-b) /8

y = a - b / 2

So, Therefore, The value of y = a + b and a - b /2

Attachments:

amitkumar44481: Perfect :-)
TheMoonlìghtPhoenix: Great!
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