Find the roots of 1/(x +4) – 1/(x-7) = 11/30.
Answers
Step-by-step explanation:
Ex 4.3 ,3 Find the roots of the following equations: (i) x – 1/=3,≠0 x ... Ex 4.3, 3 - Chapter 4 Class 10 Quadratic Equations ... 7)=11/30,≠−4, 7 1/( + 4)−1/( − 7)=11/30 (( − 7) − ( + 4))/(( +
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Step-by-step explanation:
1 Or 2 roots of given Quadratic equation.
Explanation:
Given
\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}
x+4
1
−
x−7
1
=
30
11
\implies \frac{[x-7-(x+4)]}{(x+4)(x-7)}=\frac{11}{30}⟹
(x+4)(x−7)
[x−7−(x+4)]
=
30
11
\implies\frac{x-7-x-4}{x^{2}-7x+4x-28}=\frac{11}{30}⟹
x
2
−7x+4x−28
x−7−x−4
=
30
11
\implies\frac{-11}{x^{2}-3x-28}=\frac{11}{30}⟹
x
2
−3x−28
−11
=
30
11
Do the cross multiplication, we get
=> 30 = 11(x²-3x-28)/(-11)
=> 30 = -(x²-3x-28)
=> x²-3x-28+30 =0
=> x²-3x+2=0
Splitting the middle term, we get
=> x²-1x-2x+2 =0
=> x(x-1)-2(x-1)=0
=> (x-1)(x-2)=0
=>x-1 = 0 or x-2 = 0
=> x = 1 or x = 2
Therefore,
Roots of the given quadratic equation are 1 , 2
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