If a - b -3 and ab -28- then the value of a - b is equal to-A- - 21B- - 15 - - 17D- - 11

The correct option is D ± 11Given (a b) = 3 nbsp; and ab = 28 Using identities we know that, (a+b)^2 nbsp;(a b)^2 = 4ab ⇒(a+b)^2 = nbsp;(a b)^2 + n ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a - b)^2

If a - b =3 a...

Question

If $(a - b) = 3$ and $a b = 28$ , then the value of $(a + b)$ is equal to.

\pm 21

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\pm 15

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\pm 11

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Solution

The correct option is D $\pm 11$
Given $(a - b) = 3$ and $a b = 28$

Using identities we know that,
$(a + b)^{2} - (a - b)^{2} = 4 a b$
$\Rightarrow$ $(a + b)^{2} = (a - b)^{2} + 4 a b$
$\Rightarrow$ $(a + b)^{2} = 3^{2} + 4 (28)$
$\Rightarrow$ $(a + b)^{2} = 9 + 112$
$\Rightarrow$ $(a + b)^{2} = 121$
$\Rightarrow$ $(a + b)^{2} = 11^{2}$
$\Rightarrow$ $(a + b) = \pm 11$

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If (a−b)=3 and ab=28, then the value of (a+b) is equal to.

The correct option is D ±11Given (a−b)=3 and ab=28 Using identities we know that, (a+b)2−(a−b)2=4ab ⇒(a+b)2=(a−b)2+4ab ⇒(a+b)2=32+4(28) ⇒(a+b)2=9+112 ⇒(a+b)2=121 ⇒(a+b)2=112 ⇒(a+b)=±11

If $(a - b) = 3$ and $a b = 28$ , then the value of $(a + b)$ is equal to.