Algebra
-
If √x + 4 + √x − 4 = 2 then x is equal to √x + 4 − √x − 4
-
View Hint View Answer Discuss in Forum
√x + 4 + √x − 4 = 2 √x + 4 − √x − 4 1
By componendo and dividendo,2√x + 4 = 3 2√x − 4 1
On squaring,x + 4 = 9 x − 4 1
⇒ 9x – 36 = x + 4
⇒ 9x – x = 36 + 4
⇒ 8x = 40
⇒ x = 5Correct Option: D
√x + 4 + √x − 4 = 2 √x + 4 − √x − 4 1
By componendo and dividendo,2√x + 4 = 3 2√x − 4 1
On squaring,x + 4 = 9 x − 4 1
⇒ 9x – 36 = x + 4
⇒ 9x – x = 36 + 4
⇒ 8x = 40
⇒ x = 5
- If 9√x = √12 + √147 , then x = ?
-
View Hint View Answer Discuss in Forum
9√x = √3 × 2 × 2 + √3 × 7 × 7
⇒ 9√x = 2√3 + 7√3 = 9√3
∴ x = 3Correct Option: B
9√x = √3 × 2 × 2 + √3 × 7 × 7
⇒ 9√x = 2√3 + 7√3 = 9√3
∴ x = 3
- If X * Y = X2 + Y2 – XY then 11 * 13 is
-
View Hint View Answer Discuss in Forum
X ★ ★ Y = X2 + Y2 – XY
∴ 11 ★ ★ 13 = 112 + 132 – 11 × 13
= 121 + 169 – 143 = 147Correct Option: B
X ★ ★ Y = X2 + Y2 – XY
∴ 11 ★ ★ 13 = 112 + 132 – 11 × 13
= 121 + 169 – 143 = 147
-
If 
then the value of x is
-
View Hint View Answer Discuss in Forum
Squaring both sides,1 + x = 
32 
2 = 1024 961 31 961 ⇒ x = 1024 − 1 = 1024 − 961 = 63 961 961 961 961
⇒ x = 63Correct Option: A
Squaring both sides,1 + x = 32 2 = 1024 961 31 961 ⇒ x = 1024 − 1 = 1024 − 961 = 63 961 961 961 961
⇒ x = 63
-
If √0.04 × 0.4 × a = 0.004 × 0.4 × √b, value of a is b
-
View Hint View Answer Discuss in Forum
√0.04 × 0.4 × a
= 0.004 × 0.4 × √b
Squaring both sides,
= 0.004 × 0.4 × 0.004 × 0.4 × b⇒ a = 0.004 × 0.004 × 0.4 × 0.4 = 0.00016 b 0.04 × 0.4 = 16 × 16 × 10−5 100000 Correct Option: C
√0.04 × 0.4 × a
= 0.004 × 0.4 × √b
Squaring both sides,
= 0.004 × 0.4 × 0.004 × 0.4 × b⇒ a = 0.004 × 0.004 × 0.4 × 0.4 = 0.00016 b 0.04 × 0.4 = 16 × 16 × 10−5 100000
