Question 31

Fill in the blanks to make the statement true.

$3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2} +$ ___ $= 5 x + 7 y^{2}$ .

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Solution

Let $(3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2}) + M = 5 x + 7 y^{2}$
$\Rightarrow M = (5 x + 7 y^{2}) - (3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2}) \Rightarrow M = 5 x + 7 y^{2} - 3 x - 23 x^{2} - 6 y^{2} - 2 x - y^{2}$
[With -ve sign, +ve sign in the bracket will change on opening it]
$\Rightarrow M = 5 x - 3 x - 2 x + 7 y^{2} - 6 y^{2} - y^{2} - 23 x^{2} M = 0 + 0 - 23 x^{2} = - 23 x^{2}$

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