Algebra Questions

If $x+y=12$ and $xy=6$, then the value of $\frac{x}{y}+\frac{y}{x}$ is equal to:

If $\left(x-\frac{1}{x}\right)=3$, then the value of $(x-1{)}^2+\frac{1}{(x-1{)}^2}$ is:

Simplify the given expression: $\frac{12.43\times 12.43\times 12.43+19.57\times 19.57\times 19.57}{12.43\times 12.43-12.43\times 19.57+19.57\times 19.57}$

If the average of $x$ and $\frac{1}{x}$ ($x\ne 0$) is $m$, then the average of $x^2$ and $\frac{1}{x^2}$ is :

Four distinct positive numbers, 'a', 'b', 'c' and 'd', in the order given, are in proportion. 'b' is 35 more than 'a' and 'd' is 60 more than 'c'. The product of 'a' and 'c' is 5376. What is the sum of 'a', 'b', 'c' and 'd'?

If
1+
39
x
​


​
=5, then the value of x is equal to:

Simplify the following expression:
(x+y)(x−y)(x
2
+y
2
)(x
4
+y
4
)(x
8
+y
8
)(x
1
6+y
1
6)

If x+
x
1
​
=15, then the value of (x
2
+
x
2

1
​
) is:

Two numbers are in the ratio $5:8$. If $4$ is added to each, the ratio becomes $2:3$. Find the smaller number.

The ratio of the sums of money Arun and Ahaan had is $9:5$. If Arun gives ₹$12$ from his share to Ahaan, then the ratio will change to $4:3$. How much money did Arun have initially?

Name the person who had a major influence in the field of Algebra in India.

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$, then find the two numbers?

S varies directly as (R+7), and S=42 when R=17. What is the value of S when R=29?

The LCM of two numbers is $12$ times their HCF. The sum of HCF and LCM is $1560$. If one of the numbers is $120$, then find the other number.

If the semi-perimeter and area of a rectangular field whose length and breadth are 'x' and 'y' is 12cm and 28cm
2
, respectively, then find the value of x
4
+x
2
y
2
+y
4
.

Simplify the following expression:
0.7+0.4
0.7
2
+(0.4+0.2)(0.7)+(0.4×0.2)
​

The LCM of two numbers is $495$ and their HCF is $5$. If the sum of the numbers is $100$, then find their difference.

Simplify the given expression.
(2.3)
2
+(15.9)
2
+(3.7)
2
−2.3×15.9−15.9×3.7−3.7×2.3
(2.3)
3
+(15.9)
3
+(3.7)
3
−3×2.3×15.9×3.7
​

Simplify the following expression:
4×4×4
(8.25)
3
−3×(8.25)
2
×0.25+24.75×(0.25)
2
−(0.25)
3

​

If x+y=10 and xy=12, find the value of x
2
−xy+y
2
.

Simplify $\frac{0.32\times 0.72\times 0.56}{(0.32{)}^3+(0.24{)}^3-(0.56{)}^3}$:

Find the value of $\frac{m(m^2+3m+3)+1}{m(m+2)+1}$ when $m=87$.

Simplify $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$.

If $a+b+c=1$, $ab+bc+ca=-8$ and $a^3+b^3+c^3=-11$, then what is the value of $\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}$?

What is the simplified form of the following expression?
(x−
y
1
​
)
3
+(x+
y
1
​
)
3

If a+b+c=3, ab+bc+ca=−10 and abc=−24, then the value of
bc
a
2

​
+
ac
b
2

​
+
ab
c
2

​
is:

When x is subtracted from each of the numbers 64,81,85 and 109, the numbers so obtained in this order are in proportion. What is the mean proportional between (x+3) and (2x−1)?

Simplify (x−2y)
3
−6xy(x−2y).

If a+b=2 and ab=4, then find the value of a
4
+b
4
+ab
3
+ba
3
.

If x=7−4
3

​
, then find the value of (x
2
+
x
2

1
​
).

Simplify the following expression:
33×31×(2
10
+1)
(3
2
)
4
−1
​