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1 answer:
Answer:
The value of x is 1
Step-by-step explanation:
Let us solve the question
∵ Δ PQR ≈ Δ FGH
→ From similarity, then their corresponding sides have an equal ratio
∴ =
=
∵ PQ = 3, QR = x + 3, PR = 2
∵ FG = 6, GH = 6x + 2, FH = 4
→ Substitute them in the ratios above
∴ =
=
→ By using cross multiplication between the first two ratios
∵ 3 × (6x + 2) = 6 × (x + 3)
∴ 3(6x + 2) = 6(x + 3)
∴ 3(6x) + 3(2) = 6(x) + 6(3)
∴ 18x + 6 = 6x + 18
→ Subtract 6x from both sides
∵ 18x - 6x + 6 = 6x - 6x + 18
∴ 12x + 6 = 18
→ Subtract 6 from both sides
∵ 12x + 6 - 6 = 18 - 6
∴ 12x = 12
→ Divide both sides by 12
∴ x = 1
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Answer:
1. (x - 3)² = 8
2. (x + 2)² = 3
3. (x + 6)² =
4. (x + 3)² = 27
5. (x + 4)² = 13
6.
Step-by-step explanation:
Completion of Square:
In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.
1. x² - 6x + 1 = 0
Taking the constant term to the other side, we get:
x² - 6x = - 1
⇒ x² - 2(3)x = -1
⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]
⇒ x² -2(3)x + 3² = 8
⇒ (x - 3)² = 8 is the answer.
2. 3x² + 12x + 3 = 0
Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.
3x² + 12x = -3
Dividing by 3 through out, x² + 4x = - 1
⇒ x² + 2(2) + 4 = -1 + 4
⇒ x² +2(2) + 2² = 3
⇒ (x + 2)² = 3 is the answer.
3. 2x² + 24x = 29
x² + 12x =
⇒ x² + 2(6)x + 36 = + 36
⇒ x² + 2(6)x + 6² =
⇒ (x + 6)² = is the answer.
4. x² + 6x - 18 = 0
x² + 6x = 18
⇒ x² + 2(3)x = 18
⇒ x² + 2(3)x + 9 = 18 + 9
⇒ x² + 2(3)x + 3² = 27
⇒ (x + 3)² = 27 is the answer.
5. x² + 8x + 3 = 0
x² + 8x = -3
⇒ x² + 2(4)x = -3
⇒ x² + 2(4)x + 16 = - 3 + 16
⇒ x² + 2(4)x + 16 = 13
⇒ (x + 4)² = 13 is the answer.
6. 9x² - 30x + 6 = 0
9x² - 30x = - 6
⇒ x² x = - 6
is the answer.