solve questions 15,16, and 17 pls
Answers
15) (i) (x + 1)/(x – 1) + (x – 2)/(x + 2) = 3
[(x + 1) (x + 2) + (x – 2) (x – 1)]/[(x – 1)(x + 2)] = 3 [Taking L.C.M]
On expanding, we get
x2 + 3x + 2 + x2 – 3x + 2 = 3 (x – 1) (x + 2)
2x2 + 4 = 3 (x2 + x – 2)
2x2 + 4 = 3x2 + 3x – 6
3x2 – 2x2 + 3x – 6 – 4 = 0
x2 + 3x – 10 = 0
Now, let’s factorize the above equation to find x
x2 + 5x – 2x – 10 = 0
x(x + 5) – 2(x – 5) = 0
(x + 5) (x – 5) = 0
So,
x + 5 = 0 or x – 5 = 0
x = -5 or x = 5
∴ Value of x = -5, 5
15) ii) 1/(x – 3) – 1/(x + 5) = 1/6
Taking L.C.M, we have
[x + 5 – (x – 3)] / [(x – 3) (x + 5)] = 1/6
(x + 5 – x + 3) / [(x – 3) (x + 5)] = 1/6
8/ [(x – 3) (x + 5)] = 1/6
Upon cross-multiplying, we have
8 × 6 = (x – 3) (x + 5)
48 = x2 + 5x – 3x – 15
x2 + 2x – 15 – 48 = 0
x2 + 2x – 63 = 0
Now, let’s factorize the above equation to find x
x2 + 9x – 7x – 63 = 0
x(x + 9) – 7(x + 9) = 0
(x – 7) (x + 9) = 0
So,
x – 7 = 0 or x + 9 = 0
x = 7 or x = -9
∴ Value of x = 7, -9
16) (i) a/(ax – 1) + b/(bx – 1) = a + b, a + b ≠ 0, ab ≠ 0
Let’s rearrange the equation for simple solving,
[a/(ax – 1) – b] + [b/(bx – 1) – a] = 0
[a – b(ax – 1)]/(ax – 1) + [b – a(bx – 1)]/(bx – 1) = 0
(a – abx + b)/(ax – 1) + (b – abx + a)/(bx – 1) = 0
(a – abx + b) [1/(ax – 1) + 1/(bx – 1)] = 0 {Taking common terms out}
(a – abx + b) [(bx – 1 + ax – 1)/(ax – 1)(bx – 1)] = 0
(a – abx + b) [(ax + bx – 2)/ (ax – 1)(bx – 1)] = 0
So,
(a – abx + b) = 0 or (ax + bx – 2)/ [(ax – 1) (bx – 1)] = 0
If (a – abx + b) = 0,
a + b = abx
x = (a + b)/ab
And,
if (ax + bx – 2)/ [(ax – 1) (bx – 1)] = 0
ax + bx – 2 = 0
(a + b)x = 2
x = 2/(a + b)
∴ Value of x = (a + b)/ab, 2/(a + b)
16)(ii) Answer is on the attachment
17)i). 1/(x + 6) + 1/(x – 10) = 3/(x – 4)
Taking L.C.M for the R.H.S of the equation,
[(x – 10) + (x + 6)]/ [(x + 6) (x – 10)] = 3/(x- 4)
(2x – 4)/ (x2 – 4x – 60) = 3/(x- 4)
On cross-multiplying, we get
(2x – 4) (x – 4) = 3(x2 – 4x – 60)
2x2 – 8x – 4x + 16 = 3x2 – 12x – 180
2x2 – 12x + 16 = 3x2 – 12x – 180
3x2 – 2x2 – 12x + 12x – 180 – 16 = 0
x2 – 196 = 0
x2 = 196
x = √196
∴ x = ± 14
I am also in class 10 and I have the same book.
