Question

If
$\sqrt{13 - a \sqrt{10} } = \sqrt{8} + \sqrt{5}$
Then Find the value of a.

Answer 1

Hello Mate!

Answer: Value of a is - 4.

Step-by-step explanation:

Since we know that,

( a + b )² = a² + b² + 2ab

Squaring and doing under root of √8 + √5 we get

√( √8 + √5 )² = √( 13 - a√10 )

√( 8 + 5 + 2√40 ) = √( 13 - a√10 )

√( 13 + 4√10 ) = √( 13 - a√10 )

13 + 4√10 = 13 - a√10

4√10 = - a√10

4 = - a or a = - 4

Have great future ahead!

Answer 2

☯Dearest Friend!☯



✅ Question: ✅

$\implies{ \mathsf{ { { \blue{ \sqrt{13 - a \sqrt{10} } = \sqrt{8} + \sqrt{5}}}}}}$


☯ Answer: ☯


Value of a is (-4)✅✅✅✅✅


☯ Method of Solution: ☯

$\sqrt{13 - a \sqrt{10} } = \sqrt{8} + \sqrt{5}$

$\implies{\mathsf{\sqrt{13 - a \sqrt{10} } = \sqrt{8} + \sqrt{5}}} \\ \\ \\ \\ \implies{ \mathsf{ \large{ \fbox{Squaring \: \: on \: Both \: \: Sides:}}}} \\ \\ \\ \implies{ \mathsf{ 13 - a \sqrt{10} = 8 + 5 + 2 \sqrt{40}}} \\ \\ \\ \implies{ \mathsf{ 13 - a \sqrt{10} = 13 + 2 \sqrt{40}}} \\ \\ \\ \implies{ \mathsf{ { { \red{\cancel{13} - a \sqrt{10} = { \cancel{13} + 2 \sqrt{40}}}}}}} \\ \\ \\ \\ \implies{ \mathsf{ { { \green{ - a \sqrt{10} = 4 \sqrt{10}}}}}} \\ \\ \\ \\ \implies{ \mathsf{ { { \green{ - a { \cancel{\sqrt{10}} = 4 { \cancel{\sqrt{10}}}}}}}}} \\ \\ \\ \\ \implies{ \mathsf{ { \blue{ - a = 4}}}} \\ \\ \\ \\ \implies{ \mathsf{ { \green {a = - 4}}}}$

$\implies{ \mathsf{ { { \red{Hence, Required \: Value \: of \: a \: is \: (-4)?}}}}}$