Advertisements
Advertisements
Question
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
Advertisements
Solution
y = 3x + 1
Now, 5(3x + 1)2 + 6(3x + 1) – 8 = 0
Substituting the value of 3x + 1, we get
5y2 + 6y - 8 = 0
⇒ 5y2 + 10y - 4y - 8 = 0 ...`{(∴5xx(-8) = -40),(∴ -40 = 10xx(-4)),(6 = 10 - 4):}}`
⇒ 5y(y + 2) -4(y + 2) = 0
⇒ (y + 2)(5y - 4) = 0
Either y + 2 = 0,
then y = -2
or
5y - 4 = 0,
then 5y = 4
⇒ y = `(4)/(5)`
(i) If y = -2, then
3x + 1 = -2
⇒ 3x = -2 - 1
⇒ 3x = -3
⇒ x = `(-3)/(3)`
= -1
(ii) If y = `(4)/(5)`, then
3x = 1 = `(4)/(5)`
⇒ 3x = `(4)/(5) - 1`
= `(-1)/(5)`
⇒ x = `(-1)/(5) xx (1)/(3)`
= `(-1)/(15)`
Hence x = -1, `(-1)/(15)`.
APPEARS IN
RELATED QUESTIONS
Solve for x :
`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve x2 – 4x – 12 =0; when x ∈ I
Two natural number differ by 3 and their product is 504. Find the numbers.
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
Solve the following equation by factorization
x2– 4x – 12 = 0,when x∈N
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
