Question

If the ratio of a to b is 3: 5, then find the value of
(2a² + b²) : (a² + b²).
​

Answer 1

$\huge{\tt{Given}}$

a : b = 3 : 5

$\huge{\tt{To\:Find}}$

(2 a² + b²) : (a² + b²)

$\huge{\tt{Solution}}$

Let,

a = 3 x   and

b = 5 x

then,

$\longrightarrow\rm{\dfrac{2a^2+b^2}{a^2+b^2}}\\\\\\\longrightarrow\rm{\dfrac{2(3x)^2+(5x)^2}{(3x)^2+(5x)^2}}\\\\\\\longrightarrow\rm{\dfrac{18x^2+25x^2}{9x^2+25x^2}}\\\\\\\longrightarrow\rm{\dfrac{43x^2}{34x^2}}\\\\\\\longrightarrow\large{\rm{\dfrac{43}{34}}}$

therefore,

(2a² + b²) : (a² + b²) = 43 : 34 .

Answer 2

Given a : b = 3 : 5

ToFind (2 a² + b²) : (a² + b²)

Solution

Let,

a = 3 x   and

b = 5 x

then,

\9x2+25x218x2+25x2⟶34x243x2⟶3443

therefore,

(2a² + b²) : (a² + b²) = 43 : 34 .