Algebraic Expressions and Identities Test

Result

Algebraic Expressions and Identities Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

If (3a + 4b) = 16 and ab = 4.Find the value of (9a² + 16b²)

A
160

B
100

C
120

D
140

Solution

(3a + 4b)² = 162 ⇒ 9a² + 16b² + 24ab = 256 But, ab = 4 ⇒ 9a² + 16b² + 24ab = 256 ⇒ 9a² + 16b² = 160.
Question 2
1 / -0

If (a + b + c) = 15 and (ab + bc + ca) = 74, find the value of (a² + b² + c²)

A
67

B
77

C
57

D
37

Solution

Focus on what is to be found a² + b² + c² = (a + b + c)²−2(ab + bc + ca) = (15)² − 2 × 74 = 225 −148 = 77.
Question 3
1 / -0

If (3x − 2y) = 5 and xy = 6.Find the value of 27x³ − 8y³

A
550

B
625

C
665

D
675

Solution

(3x − 2y)³ = 53 ⇒ (3x)³ − 3 × 3x × 2y(3x − 2y) − 8y³ = 125 ⇒ 27x³−18xy(3x − 2y) − 8y³ = 125 = 27x³ − 18 × 6 × 5 − 8y³ = 125 ⇒ 27x³ − 8y³ = 125 + 540 = 665.
Question 4
1 / -0

If a + b = 7and ab = 12 then what is the value of a² − ab − b²

A
12

B
13

C
14

D
−5

Solution

(a − b)² = (a + b)² − 4ab = 49 − 48 = 1 ⇒ a − b = 1 a + b = 7 a − b= 1 ⇒ a = 4,b = 3 a² − ab − b² = 16 − 12 − 9 = −5.
Question 5
1 / -0

If ab = 6 and a + b = 5, then the value of a² + b² is

A
11

B
12

C
13

D
16

Solution

a² + b² = (a + b)² − 2ab = 25 − 2 × 6 = 13.