X+1/X+3=3x+2/2x+3 : solve it using quadratic equations..help me it’s urgent. About the author Kaylee
Answer: – 3 + √6 & – 3 – √6 . Step-by-step explanation: [tex] \frac{x + 1}{x + 3} = \frac{3x + 2}{2x + 3} \\ (after \: cross \: multiplication) \\ = > x + 1(2x + 3) = x + 3(3x + 2) \\ = > x(2x + 3) + 1(2x + 3) = x(3x + 2) + 3(3x + 2) \\ = > 2 {x }^{2} + 3x + 2x + 3 = {3x}^{2} + 2x + 9x + 6 \\ = > {2x}^{2} + 5x + 3 = {3x}^{2} + 11x + 6 \\ = > 5x + 3 = {3x}^{2} – {2x}^{2} + 11x + 6 \\ = > 3 = {x}^{2} + 11x – 5x + 6 \\ = > 0 = {x}^{2} + 6x + 6 – 3 \\ = > {x}^{2} + 6x + 3 = 0[/tex] Now it is the standard form of quadratic equation (ax² + bx + c), here a = 1 b = 6 c = 3 We will find the roots of the quadratic equation, [tex]roots \: = \frac{ – b ± \sqrt{ {b}^{2} – 4ac } }{2a} \\ = > \frac{ – 6 ± \sqrt{( {6)}^{2} – 4(1)(3)} }{2(1)} \\ = > \frac{ – 6 ± \sqrt{36 – 12} }{2} \\ = > \frac{ – 6 ± \sqrt{24} }{2} \\ = > \frac{ – 6 ± 2 \sqrt{6} }{2} \\ = > – 3 ± \sqrt{6} \\ roots = – 3 + \sqrt{6} \\ – 3 – \sqrt{6} [/tex] Hence the value of x = –3 + √6 & –3 – √6 hope it helps. Reply
Answer:
– 3 + √6 & – 3 – √6
.
Step-by-step explanation:
[tex] \frac{x + 1}{x + 3} = \frac{3x + 2}{2x + 3} \\ (after \: cross \: multiplication) \\ = > x + 1(2x + 3) = x + 3(3x + 2) \\ = > x(2x + 3) + 1(2x + 3) = x(3x + 2) + 3(3x + 2) \\ = > 2 {x }^{2} + 3x + 2x + 3 = {3x}^{2} + 2x + 9x + 6 \\ = > {2x}^{2} + 5x + 3 = {3x}^{2} + 11x + 6 \\ = > 5x + 3 = {3x}^{2} – {2x}^{2} + 11x + 6 \\ = > 3 = {x}^{2} + 11x – 5x + 6 \\ = > 0 = {x}^{2} + 6x + 6 – 3 \\ = > {x}^{2} + 6x + 3 = 0[/tex]
Now it is the standard form of quadratic equation (ax² + bx + c), here
a = 1
b = 6
c = 3
We will find the roots of the quadratic equation,
[tex]roots \: = \frac{ – b ± \sqrt{ {b}^{2} – 4ac } }{2a} \\ = > \frac{ – 6 ± \sqrt{( {6)}^{2} – 4(1)(3)} }{2(1)} \\ = > \frac{ – 6 ± \sqrt{36 – 12} }{2} \\ = > \frac{ – 6 ± \sqrt{24} }{2} \\ = > \frac{ – 6 ± 2 \sqrt{6} }{2} \\ = > – 3 ± \sqrt{6} \\ roots = – 3 + \sqrt{6} \\ – 3 – \sqrt{6} [/tex]
Hence the value of x = –3 + √6 & –3 – √6
hope it helps.