Find the sum of the following surds

(1)

(2)

(3)

Q.

Find the sum of the following polynomials and write the degree of the sum so obtained

(i) 2x³ $-$ 7x² + 3x + 4 ; 2x³ $-$ 3x² + 4x + 1
(ii) 3x² + 5x $-$ x⁷ ; $-$ 3x² + 5x + 8
(iii) x⁴ + 5x³ + 7x ; 4x³ $-$ 3x² + 5
(iv) y² + 2y $-$ 5 ; y³ + 2y² + 3y + 4 ; y³ + 7y $-$ 2
(v) 5m² + 3m + 8 ; m³ $-$ 6m² + 4m ; m³ $-$ m² $-$ m + 5

Q. Solve the following equations by Cramer’s method.
(1) 6x – 3y = –10 ; 3x + 5y – 8 = 0
(2) 4m – 2n = –4 ; 4m + 3n = 16
(3) 3x – 2y = $\frac{5}{2}$ ; $\frac{1}{3}x+3y=-\frac{4}{3}$
(4) 7x + 3y = 15 ; 12y – 5x = 39
(5) $\frac{x+y-8}{2}=\frac{x+2y-14}{3}=\frac{3x-y}{4}$

Q.

Which of the following pairs of linear equations is inconsistent?
$1.x+3y–5=0,2x+y=0$
$2.2x+y=1,2y=2–4x$
$3.2x–y=2,2y–4x=2$

Q. Factorize the following:
2x³y² − 4x²y³ + 8xy⁴

Q. Range of rational expression $y=\frac{x^2-x+4}{x^2+x+4},x\in R$ is