Question
$$9{x^2} + 25 - 30x$$ can be expressed as the square of = ?
Answer: Option D
$$\eqalign{
& {\text{We have to find}} \cr
& = \sqrt {9{x^2} + 25 - 30x} \cr} $$
$$ = \sqrt {{{\left( {3x} \right)}^2} - 2.3x.5 + {{\left( { - 5} \right)}^2}} $$
$$\,\,\,\,\,\,\,\left\{ {\because {a^2} - 2ab + {b^2} = {{\left( {a + b} \right)}^2}} \right\}$$
$$\eqalign{
& = \sqrt {{{\left( {3x - 5} \right)}^2}} \cr
& = 3x - 5 \cr} $$
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$$\eqalign{
& {\text{We have to find}} \cr
& = \sqrt {9{x^2} + 25 - 30x} \cr} $$
$$ = \sqrt {{{\left( {3x} \right)}^2} - 2.3x.5 + {{\left( { - 5} \right)}^2}} $$
$$\,\,\,\,\,\,\,\left\{ {\because {a^2} - 2ab + {b^2} = {{\left( {a + b} \right)}^2}} \right\}$$
$$\eqalign{
& = \sqrt {{{\left( {3x - 5} \right)}^2}} \cr
& = 3x - 5 \cr} $$
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