SSC GD Constable 5 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 59 of 80

Marks: +1, -0

Find the third proportional of (3 + √2) and 2√7.

Solution:

a, b

, and c are in continued proportion, then

b ^2= a × c

Calculation:
Let the third proportional be c .

\;2 {√{ }} 7)^2=(3+{√{ }} 2) × c

\;⇒ 4 × 7=(3+{√{ }} 2) × c

\;⇒ 28=(3+{√{ }} 2) × c

\;⇒ c=\;{28}/{3+{√{ }} 2}

Rationalize the denominator:

\;⇒ c=\;{28}/{3+{√{2}}} × \;{3-{√{2}}}/{3-{√{2}}}

\;⇒ c=\;{28(3-{√{2}})}/{9-2}

\;⇒ c=\;{28(3-{√{2}})}/{7}

\;⇒ c=4(3-{√{2}})

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