Question 1. [3+3+4]
(a) Find the expansion of the following: (x + y – 1)3
(b) Factorise the following: x4 + 5x2 + 9.
(c) Solve the following pairs of linear equations:
+
+
−
= 3;
+
+
−
=
.
Question 2. [3+3+4]
(a) Multiply (9x2 + 25y2 + 15xy + 12x – 20y + 16) by (3x – 5y – 4), using a suitable identity.
(b) Solve the following pairs of linear equations by cross-multiplication method:
2bx + ay = 2ab ; bx – ay = 4ab.
(c) Solve: 2x -
= 9; 3x +
= 2. Hence find the value of k if x = k y + 5.
Question 3. [3+3+4]
(a) If a2 – 3a + 1 = 0, find a2 +
.
(b) Factorise the following: (x2 – 2x)2 – 23(x2 – 2x) + 120.
(c) A two-digit number is such that the ten’s digit exceeds twice the unit’s digit by 2 and the number
obtained by inter-changing the digits is 5 more than three times the sum of the digits. Find the two digit
number.
Question 4. [3+3+4]
(a) If a + b + c = 2, ab + bc + ca = - 1 and abc = -2, find the value of a3 + b3 + c3
.
(b) Solve the following system of simultaneous linear equations by elimination method:
9 – (x – 4) = y + 7; 2 (x + y) = 4 – 3y.
(c) 3 men and 4 boys can do a piece of work in 14 days, while 4 men and 6 boys can do it in 10 days. How
long would it take 1 boy to finish the work ?
Question 5. [3+3+4]
(a) Solve the following system of simultaneous linear equations by substitution method:
2x -
= 3; 5x – 2y – 7 = 0.
(b) Factorise the following: a3 – 3a2b + 3ab2 – 2b3
.
(c) A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48 minutes longer to cover
the same distance against the current. Find the speed of the boat in still water and the speed of the current.
Answers
Answered by
20
Factorise the following: (x² – 2x)² – 23(x² – 2x) + 120
Step-by-step explanation:
(x² – 2x)² – 23(x² – 2x) + 120
- a = (x² – 2x)
a² – 23a + 120
a² - 15a - 8a + 120
a(a - 15) - 8(a - 15)
(a - 15) (a - 8)
a = 15 or 8
x² - 2x = 15 or x² - 2x = 8
x² - 2x - 15 = 0 or x² - 2x - 8 = 0
(x - 5)(x + 3) = 0 or (x - 4) (x + 2) = 0
So the final answer is
(x - 5) (x + 3) (x - 4) (x + 2) = 0
Answered by
1
Answer:
hi
Step-by-step explanation:
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